Deck 16: Multiple Regression Model Building

Question 1

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ?₀ + ?₁X + ?₂X² + ^?
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
$\begin{array}{|l|l|l|l|l|l|}\text { SUMMARY } &output & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12\\\hline\\\hline\text { ANOVA }\\\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & &\\\hline\\\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline\end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-2,what is the value of the test statistic for testing whether the quadratic term is necessary in fitting in the response curve relating the demand (Y)and the price (X)?

A)-5.14
B)0.95
C)373
D)None of the above.

Answer 1

0.95

Question 2

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic curvilinear relationship between time and dose.The value of the test statistic is ________.

Answer 2

2.312 or 5.3361

Question 3

Instruction 16-1
To explain personal consumption (CONS)measured in dollars,data is collected for
$$\begin{array}{l}\begin{array} {|l|l|} \hline \text {INC }&\text { personal income in dollars}\\\hline&\text {\( \$ 1 \) plus the credit limit in dollars available to the }\\\text { CRDTLIM}&\text { individual}\\\hline&\text {average annualised percentage interest rate for }\\\text {APR: }&\text {borrowing for the individual }\\\hline&\text {per person advertising expenditure in dollars by }\\&\text { manufacturers in the city where the }\\\text {ADVT: }&\text {individual lives }\\\hline\text {GENDER:}&\text {gender of the individual; 1 if female, 0 if male}\\\hline \end{array}\end{array}$$ A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was
= 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER

-Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for APR?

A)A 1% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant.
B)A one percentage point increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant.
C)A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant.
D)A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant.

Answer 3

A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant.

Question 4

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ?₀ + ?₁X + ?₂X² + ^?
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
$\begin{array}{|l|l|l|l|l|l|}\text { SUMMARY } &output & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12\\\hline\\\hline\text { ANOVA }\\\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & &\\\hline\\\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline\end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-2,what is the p-value associated with the test statistic for testing whether the quadratic term is necessary in fitting the response curve relating the demand (Y)and the price (X)?

A)0.0001
B)0.0006
C)0.3647
D)None of the above.

Question 5

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
$\begin{array}{l|l|l|l|l|l|}\text { SUMMARY } & output& \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.747 \\\hline \text { R Square } & & 0.558 \\\hline \text { Adj. R Square } & & 0.478 \\\hline \text { Std. Error } & 363.1 \\\hline \text { Observations } & 14 \\\hline\\\hline \text { ANOVA } & & & & & \\\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Sign?f } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\hline \text { Residual } & 11 & 8193929 & 744903 & & \\\hline \text { Total } & 13 & 18538726 & & & \\\hline\\\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\\hline\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error

-Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic relationship between time and dose.If she chooses to use a level of significance of 0.05,she would decide that there is a significant curvilinear relationship.

Question 6

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a quadratic curvilinear model that includes a linear term.The p-value of the test statistic for the contribution of the quadratic curvilinear term is ________.

Question 7

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic relationship between time and dose.The p-value of the test is ________.

Question 8

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
$\begin{array}{l|l|l|l|l|l|}\text { SUMMARY } & output& \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.747 \\\hline \text { R Square } & & 0.558 \\\hline \text { Adj. R Square } & & 0.478 \\\hline \text { Std. Error } & 363.1 \\\hline \text { Observations } & 14 \\\hline\\\hline \text { ANOVA } & & & & & \\\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Sign?f } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\hline \text { Residual } & 11 & 8193929 & 744903 & & \\\hline \text { Total } & 13 & 18538726 & & & \\\hline\\\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\\hline\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error

-Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if the linear term is significant.Using a level of significance of 0.05,she would decide that the quadratic model should include a linear term.

Question 9

So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

Question 10

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
$\begin{array}{l|l|l|l|l|l|}\text { SUMMARY } & output& \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.747 \\\hline \text { R Square } & & 0.558 \\\hline \text { Adj. R Square } & & 0.478 \\\hline \text { Std. Error } & 363.1 \\\hline \text { Observations } & 14 \\\hline\\\hline \text { ANOVA } & & & & & \\\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Sign?f } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\hline \text { Residual } & 11 & 8193929 & 744903 & & \\\hline \text { Total } & 13 & 18538726 & & & \\\hline\\\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\\hline\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error

-Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a quadratic model that includes a linear term.If she used a level of significance of 0.05,she would decide that the linear model is sufficient.

Question 11

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

Question 12

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ?₀ + ?₁X + ?₂X² + ^?
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
$\begin{array}{|l|l|l|l|l|l|}\text { SUMMARY } &output & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12\\\hline\\\hline\text { ANOVA }\\\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & &\\\hline\\\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline\end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-2,does the quadratic term appear to be significant in the response curve relating the demand (Y)and the price (X)at 10% level of significance?

A)No,sine the value of ?₂ is near 0.
B)No,since the p-value for the test is greater than 0.10.
C)Yes,since the p-value for the test is less than 0.10.
D)Yes,since the value of ?₂ is positive.

Question 13

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ?₀ + ?₁X + ?₂X² + ^?
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
$\begin{array}{l|l|l|l|l|l|}\hline \text { SUMMARY } & & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12 \\\hline\\\hline\text { ANOVA }\\\hline& \text { If } & \text { SS } & \text { MS } & F & \text { Sig?f F } \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & & \\\hline\\\hline& \text { Coeff } & \text { StdError } & \text { Stat } & P \text {-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & 0.31 & 0.06 & -5.14 & 0.0006 \\\hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647\\\hline\end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-2,and noting that this model includes both a linear and a quadratic term,what is the correct interpretation of the coefficient of multiple determination?

A)98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B)98.8% of the total variation in demand can be explained by the addition of the square term in price.
C)98.8% of the total variation in demand can be explained by just the square term in price.
D)98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.

Question 14

Instruction 16-2
A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = ?₀ + ?₁X + ?₂X² + ^?
where Y = demand (in thousands)and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below:
$\begin{array}{|l|l|l|l|l|l|}\text { SUMMARY } &output & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.994 \\\hline \text { R Square } & & 0.988 \\\hline \text { Std. Error } & & 12.42 \\\hline \text { Observations } & & 12\\\hline\\\hline\text { ANOVA }\\\hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\\hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\\hline \text { Residual } & 9 & 1388 & 154 & & \\\hline \text { Total } & 11 & 116533 & & &\\\hline\\\hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\\hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\\hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\\hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline\end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-2,a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).

Question 15

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
$\begin{array}{l|l|l|l|l|l|}\text { SUMMARY } & output& \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.747 \\\hline \text { R Square } & & 0.558 \\\hline \text { Adj. R Square } & & 0.478 \\\hline \text { Std. Error } & 363.1 \\\hline \text { Observations } & 14 \\\hline\\\hline \text { ANOVA } & & & & & \\\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Sign?f } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\hline \text { Residual } & 11 & 8193929 & 744903 & & \\\hline \text { Total } & 13 & 18538726 & & & \\\hline\\\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\\hline\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error

-Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic relationship between time and dose.If she chooses to use a level of significance of 0.01 she would decide that there is a significant quadratic relationship.

Question 16

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
$\begin{array}{l|l|l|l|l|l|}\text { SUMMARY } & output& \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.747 \\\hline \text { R Square } & & 0.558 \\\hline \text { Adj. R Square } & & 0.478 \\\hline \text { Std. Error } & 363.1 \\\hline \text { Observations } & 14 \\\hline\\\hline \text { ANOVA } & & & & & \\\hline & \text { df } & \text { SS } & \text { MS } & F & \text { Sign?f } F \\\hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\\hline \text { Residual } & 11 & 8193929 & 744903 & & \\\hline \text { Total } & 13 & 18538726 & & & \\\hline\\\hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\\hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\\hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\\hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\\hline\end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error

-Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a quadratic model that includes a linear term.If she used a level of significance of 0.01,she would decide that the linear model is sufficient.

Question 17

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
Referring to Instruction 16-5,the prediction of time to relief for a person receiving a dose of the drug 10 units above the average dose ,is ________.

Question 18

One transformation that may help overcome violations to the assumption of equal variance is the square-root transformation.

Question 19

Instruction 16-1
To explain personal consumption (CONS)measured in dollars,data is collected for
$$\begin{array}{l}\begin{array} {|l|l|} \hline \text {INC }&\text { personal income in dollars}\\\hline&\text {\( \$ 1 \) plus the credit limit in dollars available to the }\\\text { CRDTLIM}&\text { individual}\\\hline&\text {average annualised percentage interest rate for }\\\text {APR: }&\text {borrowing for the individual }\\\hline&\text {per person advertising expenditure in dollars by }\\&\text { manufacturers in the city where the }\\\text {ADVT: }&\text {individual lives }\\\hline\text {GENDER:}&\text {gender of the individual; 1 if female, 0 if male}\\\hline \end{array}\end{array}$$ A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was
= 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER

-Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for ADVT?

A)A 1% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant.
B)A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant.
C)A $1 increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant.
D)A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant.

Question 20

Instruction 16-5
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow.
Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error
Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a quadratic model without a linear term and a quadratic model that includes a linear term.The value of the test statistic is ________.

Question 21

The logarithm transformation can be used

A)to test for possible violations to the autocorrelation assumption.
B)to change a linear independent variable into a nonlinear independent variable.
C)to change a nonlinear model into a linear model.
D)to overcome violations to the autocorrelation assumption.

Question 22

In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

Question 23

One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

Question 24

Cook's Distance Statistic can be used to analyze the influence of individual data points.

Question 25

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

Question 26

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Question 27

Two simple regression models were used to predict a single dependent variable.Both models were highly significant,but when the two independent variables were placed in the same multiple regression model for the dependent variable,R² did not increase substantially and the parameter estimates for the model were not significantly different from 0.This is probably an example of collinearity.

Question 28

Applying a transformation to a data set,original values of Y of 1.6 and 4.2 become transformed values of 11.5 and 33.9.What transformation was used?

Question 29

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Question 30

Evaluating the influence of individual data points using a studentized deleted residual test is usually done with a one-tailed t-test.

Question 31

For a model with 5 independent variables and data set with 50 observations,the numerator degrees of freedom for the Cook's Distance Statistic would be 4.

Question 32

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Question 33

Using the C_p statistic in model building,all models with C_p ≤ (k + 1)are equally good.

Question 34

The parameter estimates are biased when collinearity is present in a multiple regression equation.

Question 35

The stepwise regression approach takes into consideration all possible models.

Question 36

The logarithm transformation can be used

A)to test for possible violations to the autocorrelation assumption.
B)to overcome violations to the autocorrelation assumption.
C)to overcome violations to the homoscedasticity assumption.
D)to test for possible violations to the homoscedasticity assumption.

Question 37

Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Question 38

Calculating Cook's Distance Statistic requires the use of matrix algebra.

Question 39

Which of the following will NOT change a nonlinear model into a linear model?

A)Logarithmic transformation.
B)Square-root transformation.
C)Variance inflationary factor .
D)Quadratic regression model.

Question 40

In data mining where huge data sets are being explored to discover relationships among a large number of variables,the best-subsets approach is more practical than the stepwise regression approach.

Question 41

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₄ should be dropped to remove collinearity.

Question 42

Instruction 16-3
In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a
cove.Model 1: Y = ? 0 + ? 1X1 + ? 2X2 + ? 3X1X2 + ? 4+ ? 5X2 + ? where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
X2 = 1 if property located near cove,0 if not
Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown:
$\begin{array}{|l|l|l|l|l|l|}\hline \text { SUMMARY } & \text { OUTPUT } & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.985 \\\hline \text { R Square } & & 0.970 \\\hline \text { Std. Error } & & 9.5 \\\hline \text { Observations } & & 20 \\\hline\\\hline\text { ANOVA }\\\hline & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\hline \text { Regression } & 5 & 28324 & 5664 & 62.2 & 0.0001 \\\hline \text { Residual } & 14 & 1279 & 91 & & \\\hline \text { Total } & 19 & 29603 & & & \\\hline\\\hline&\text {Coeff }&\text {StdError }&\text {t stat }&\text { P-Value}\\\hline \text { Intercept } & -32.1 & 35.7 & -0.90 & 0.3834 \\\hline \text { Size } & 12.2 & 5.9 & 2.05 & 0.0594 \\\hline \text { Cove } & -104.3 & 53.5 & -1.95 & 0.0715 \\\hline \text { Size }{ }^{*} \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \\\hline \text { SizeSq } & -0.3 & 0.2 & -1.28 & 0.2204 \\\hline \text { SizeSq } & -0.3 & 0.3 & -1.13 & 0.2749 \\\hline \end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-3,given a quadratic relationship between sale price (Y)and property size (X1),what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?

A)H₀: ?₂ = 0
B)H₀: ?₃ = ?₅ = 0
C)H₀: ?₄ = ?₅ = 0
D)H₀: ?₂ = ?₃ = ?₅ = 0

Question 43

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₆ should be dropped to remove collinearity.

Question 44

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₅ should be dropped to remove collinearity.

Question 45

Instruction 16-3
In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a
cove.Model 1: Y = ? 0 + ? 1X1 + ? 2X2 + ? 3X1X2 + ? 4+ ? 5X2 + ? where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
X2 = 1 if property located near cove,0 if not
Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown:
$\begin{array}{|l|l|l|l|l|l|}\hline \text { SUMMARY } & \text { OUTPUT } & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.985 \\\hline \text { R Square } & & 0.970 \\\hline \text { Std. Error } & & 9.5 \\\hline \text { Observations } & & 20 \\\hline\\\hline\text { ANOVA }\\\hline & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\hline \text { Regression } & 5 & 28324 & 5664 & 62.2 & 0.0001 \\\hline \text { Residual } & 14 & 1279 & 91 & & \\\hline \text { Total } & 19 & 29603 & & & \\\hline\\\hline&\text {Coeff }&\text {StdError }&\text {t stat }&\text { P-Value}\\\hline \text { Intercept } & -32.1 & 35.7 & -0.90 & 0.3834 \\\hline \text { Size } & 12.2 & 5.9 & 2.05 & 0.0594 \\\hline \text { Cove } & -104.3 & 53.5 & -1.95 & 0.0715 \\\hline \text { Size }{ }^{*} \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \\\hline \text { SizeSq } & -0.3 & 0.2 & -1.28 & 0.2204 \\\hline \text { SizeSq } & -0.3 & 0.3 & -1.13 & 0.2749 \\\hline \end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-3,is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?

A)Yes,since the p-value for the test is smaller than 0.05.
B)No,since some of the t tests for the individual variables are not significant.
C)No,since the standard deviation of the model is fairly large.
D)Yes,since none of the ?-estimates are equal to 0.

Question 46

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₂,X₃,X₅ and X₆ should be selected using the adjusted r² statistic.

Question 47

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

Question 48

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₃,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

Question 49

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₂,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

Question 50

Instruction 16-3
In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a
cove.Model 1: Y = ? 0 + ? 1X1 + ? 2X2 + ? 3X1X2 + ? 4+ ? 5X2 + ? where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
X2 = 1 if property located near cove,0 if not
Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown:
$\begin{array}{|l|l|l|l|l|l|}\hline \text { SUMMARY } & \text { OUTPUT } & \\\hline \text { Regression } & \text { Statistics } & \\\hline \text { Multiple R } & & 0.985 \\\hline \text { R Square } & & 0.970 \\\hline \text { Std. Error } & & 9.5 \\\hline \text { Observations } & & 20 \\\hline\\\hline\text { ANOVA }\\\hline & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\\hline \text { Regression } & 5 & 28324 & 5664 & 62.2 & 0.0001 \\\hline \text { Residual } & 14 & 1279 & 91 & & \\\hline \text { Total } & 19 & 29603 & & & \\\hline\\\hline&\text {Coeff }&\text {StdError }&\text {t stat }&\text { P-Value}\\\hline \text { Intercept } & -32.1 & 35.7 & -0.90 & 0.3834 \\\hline \text { Size } & 12.2 & 5.9 & 2.05 & 0.0594 \\\hline \text { Cove } & -104.3 & 53.5 & -1.95 & 0.0715 \\\hline \text { Size }{ }^{*} \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \\\hline \text { SizeSq } & -0.3 & 0.2 & -1.28 & 0.2204 \\\hline \text { SizeSq } & -0.3 & 0.3 & -1.13 & 0.2749 \\\hline \end{array}$ Note: Std.Error = Standard Error

-Referring to Instruction 16-3,given a quadratic relationship between sale price (Y)and property size (X1),what test should be used to test whether the curves differ from cove and non-cove properties?

A)F test for the entire regression model.
B)Partial F test on the subset of the appropriate coefficients.
C)t test on each of the subsets of the appropriate coefficients.
D)t test on each of the coefficients in the entire regression model.

Question 51

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Age?

Question 52

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes all six independent variables should be selected using the adjusted r² statistic.

Question 53

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₁ should be dropped to remove collinearity.

Question 54

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₃ should be dropped to remove collinearity.

Question 55

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the variable X₂ should be dropped to remove collinearity.

Question 56

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Edu?

Question 57

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₂,X₃,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

Question 58

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.

Question 59

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes all six independent variables should be selected using the Mallow's C_p statistic.

Question 60

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:
$$\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5?6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \times 1 \times 2 \times 5 \times 6 & 0.4697 & 0.4091 & 18.3919 \\\hline \times 1 \times 3 \times 5 \times 6 & 0.4691 & 0.4084 & 18.4023 \\\hline \times 1 \times 2 \times 3 \times 5 \times 6 & 0.4877 & 0.4123 & 18.3416 \\\hline \times 1 \times 2 \times 3 \times 4 \times 5 \times 6 & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$$

-Referring to Instruction 16-6,the model that includes X₁,X₅ and X₆ should be selected using the adjusted r² statistic.

Question 61

In multiple regression,the ________ procedure permits variables to enter and leave the model at different stages of its development.

A)stepwise regression
B)forward selection
C)backward elimination
D)residual analysis

Question 62

Which of the following is used to determine observations that have influential effect on the fitted model?

A)Variance inflationary factor.
B)The C_p statistic.
C)Cook's distance statistic.
D)Durbin Watson statistic.

Question 63

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Job Y_r?

Question 64

A regression diagnostic tool used to study the possible effects of collinearity is

A)the VIF.
B)the Y-intercept.
C)the standard error of the estimate.
D)the slope.

Question 65

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Manager?

Question 66

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₃,X₅ and X₆?

Question 67

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to

A)collinearity.
B)the absence of dummy variables.
C)the presence of dummy variables.
D)autocorrelation.

Question 68

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Married?

Question 69

As a project for his business statistics class,a student examined the factors that determined parking metre rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesised is Y_i = α + β₁x_1i + β₂x_2i + β₃x_3i + ε_i
Where
Y is the metre price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the metre is located in downtown
And off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the metre is located outside of
Downtown and off campus,and the value 0 otherwise
Suppose that whether the metre is located on campus is an important explanatory factor.Why should the variable that depicts this attribute not be included in the model?

A)Its inclusion will introduce autocorrelation.
B)Its inclusion will inflate the standard errors of the estimated coefficients.
C)Its inclusion will introduce collinearity.
D)Both B and C.

Question 70

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₂,X₅ and X₆?

Question 71

The Variance Inflationary Factor (VIF)measures the

A)standard deviation of the slope.
B)contribution of each X variable with the Y variable after all other X variables are included in the model.
C)correlation of the X variables with the Y variable.
D)correlation of the X variables with each other.

Question 72

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₅ and X₆?

Question 73

The C_p statistic is used

A)to determine if there is a problem of collinearity.
B)to choose the best model.
C)to determine if there is an irregular component in a time series.
D)if the variances of the error terms are all the same in a regression model.

Question 74

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the variance inflationary factor of Head of Household?

Question 75

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending.What should the microeconomist who developed this multiple regression model be particularly concerned with?

A)Normality of residual.
B)Randomness of error terms.
C)Missing observations.
D)Collinearity.

Question 76

A real estate builder wishes to determine how house size (House)is influenced by family income (Income),family size (Size),and education of the head of household (School).House size is measured in hundreds of square metres,income is measured in thousands of dollars,and education is in years.The builder randomly selected 50 families and developed a multiple regression model.The business literature involving human capital shows that education influences an individual's annual income.Combined,these may influence family size.With this in mind,what should the real estate builder be particularly concerned with when analysing the multiple regression model?

A)Normality of residuals.
B)Collinearity.
C)Missing observations.
D)Randomness of error terms.

Question 77

Which of the following is used to find a "best" model?

A)Standard error of the estimate.
B)Adjusted r².
C)Odds ratio.
D)Mallow's C_p.

Question 78

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes all the six independent variables?

Question 79

Instruction 16-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no).
The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_j as the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993.
The partial results from best-subset regression are given below:

Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₂,X₃,X₅ and X₆?

Question 80

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

A)The C_p statistic.
B)The studentised deleted residuals t_i.
C)The hat matrix elements h_i.
D)Cook's distance statistic.