Deck 17: Model Building

Question 1

True or False Data transformation may include converting x to its square root or inverse.

Answer 1

True

Question 2

The model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ is not suitable when

A) the relationship between y and x is linear.
B) the relationship between y and x is nonlinear.
C) the coefficientsandare independent of one another.
D) the coefficientsandare dependent of one another.

Answer 2

the relationship between y and x is nonlinear.

Question 3

The second-order polynomial model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ allows the plotted line to reverse the direction in which it is curving.

Answer 3

False

Question 4

The exponential model $\hat { Y }$ = b₀b₁^x can be converted to a linear model by taking the logarithms of both sides of the equation (either natural or common logarithms can be used as long as we are consistent).

Question 5

True or False A practical way to identify multicollinearity is to generate a standard deviation matrix.

Question 6

True or False A qualitative variable such as gender can be included in regression analysis and is referred to as a dummy variable.

Question 7

Consider the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ .The slope of the relationship between $E ( y )$ and $x _ { 1 }$

A) is constant for all values of x₂.
B) depends on the value of x₂.
C) depends on the value of x₁.
D) is constant for all values of x₁.

Question 8

True or False If the goal for the regression analysis is to interpret partial regression coefficients in an attempt to better understand the relationship between the dependent variable and one or more of the predictor variables,it will be desirable to build a smaller model with predictor variables that are more independent from each other.

Question 9

True or False The coefficient of determination R² for the third-order polynomial model is always larger than R² for the second-order polynomial model.

Question 10

Interaction between two predictor variables is present when the effect on E(y)of a 1-unit increase in $x _ { 2 }$ does not depend on the value of $x _ { 1 }$ ,and vice versa.

Question 11

The model $\mathrm { y } _ { \mathrm { i } } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { i } + \beta _ { 2 } \mathrm { x } _ { i } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { i } ^ { 3 } + \ldots \ldots + \beta _ { y } \mathrm { x } _ { \mathrm { i } } ^ { \mathrm { p } } + \epsilon _ { 1 }$ is referred to as a:

A) polynomial model with one predictor variable.
B) polynomial model with p predictor variables.
C) polynomial model with (p + 1)predictor variables.
D) polynomial model with (x +1)predictor variables.

Question 12

True or False If level of education has four possible categories,four qualitative variables would be needed to represent education in the regression model.

Question 13

The model $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂ is used whenever the statistician believes that:

A) E(y)is linearly related to x₁ and the predictor variables do not interact.
B) E(y)is linearly related to x₂ and the predictor variables do not interact.
C) Either A or B is correct.
D) Both A and B are correct.

Question 14

True or False The first-order polynomial model is the same as the simple linear regression model.

Question 15

For the second-order polynomial model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ ,the shape of the curve will be determined by the relative sizes of $\beta _ { 1 }$ and $\beta _ { 2 }$ and on their signs.

Question 16

True or False In general,we should attempt to use the simplest possible model that satisfies the goal for which the model is being developed.

Question 17

True or False Multicollinearity is a situation in which the dependent variable is highly correlated with two or more of the independent variables in a multiple regression.

Question 18

The model $\hat { Y }$ = b₀ + b₁x + b₂x² is referred to as a:

A) simple linear regression model.
B) first order model with one predictor variable.
C) second order model with one predictor variable.
D) third order model with one predictor variable.

Question 19

The model $\hat { Y }$ = $b _ { 0 } x _ { 1 } ^ { b } 1 x _ { 2 } ^ { b _ { 2 } }$ is referred to as a multiplicative model with two predictor variables.

Question 20

True or False If two or more independent variables are highly correlated with each other,multicollinearity is present,and the partial regression coefficients will be unreliable.

Question 21

In general,to represent a qualitative predictor variable that has n possible categories we must create:

A) (n + 2)qualitative variables.
B) (n + 1)qualitative variables.
C) n qualitative variables.
D) (n - 1)qualitative variables.

Question 22

In a first-order model with two predictors x₁ and x₂,an interaction term may be used when:

A) the effect of x₁ on the dependent variable is influenced by x_2.
B) the effect of x₂ on the dependent variable is influenced by x_1.
C) the relationship between the dependent variable and the independent variables is linear.
D) Both A and B are correct.

Question 23

In forward selection stepwise regression with ten predictor variables,which of the following statements is correct?

A) The procedure starts with 10 predictor variables and eliminate one predictor at each iteration.
B) The procedure starts with 2 predictor variables and add one predictor at each iteration.
C) The procedure starts with 1 predictor variable and add one predictor at each iteration.
D) The procedure starts with no predictor variables and add one predictor at each iteration.

Question 24

Consider the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }$ .Which term provides a nonlinear component to the model allowing the line to curve?

A) $\beta _ { 0 }$
B) $\beta _ { 1 } x$
C) $\beta _ { 2 } x ^ { 2 }$
D) $\beta _ { 3 } x ^ { 3 }$

Question 25

The model $\hat{ Y }$ = b₀ + b₁x₁ + b₂x₂ is referred to as the:

A) first order model with one predictor variable.
B) first order model with two predictor variables.
C) second order model with one predictor variable.
D) second order model with two predictor variables.

Question 26

The shape of the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ could be:

A) parabolic resembling an upright"U".
B) parabolic resembling an upside-down"U".
C) a straight line with an intercept $\beta _ { 0 }$ and slope $\beta _ { 2 } / \beta _ { 1 }$ .
D) a straight line with an intercept $\beta _ { 0 }$ and slope $\beta _ { 1 } / \beta _ { 2 } .$ .
E) Both A and B.

Question 27

Consider the first-order regression model $\hat{ y }$ = 15 + 6x₁ + 5x₂ + 4x₁x₂. A unit increase in x1 increases the value of y on average by:

A) 5.
B) 30.
C) 26.
D) an amount that depends on the value of x₂.

Question 28

Multicollinearity in a regression model can be detected when

A) two or more independent variables are highly correlated with each other.
B) an independent variable known to be an important predictor ends up having a partial regression coefficient that is not significant.
C) a partial regression coefficient that should be positive turns out to be negative,or vise versa.
D) when an independent variable is added or removed ,the partial regression coefficients for the other independent variables change drastically.
E) All of the above could be evidence that multicollinearity is present in the model.

Question 29

In explaining students' test scores,which of the following independent variables would not best be represented by a dummy variable?

A) Gender
B) Race
C) Number of hours studying for the test
D) Marital status

Question 30

In explaining the income earned by college graduates,which of the following independent variables is best represented by a dummy variable?

A) Grade point average
B) Age
C) Number of years since graduating from high school
D) College major

Question 31

Consider the model described by the equation $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }$$ .Which term provides a nonlinear component to the model enabling the line to reverse the direction of curvature?

A) $\beta _ { 0 }$
B) $\beta _ { 1 } x$
C) $\beta _ { 2 } x ^ { 2 }$
D) $\beta _ { 3 } x ^ { 3 }$

Question 32

In regression analysis,qualitative variables are sometimes referred to as:

A) response variables.
B) dummy variables.
C) nonsense variables.
D) dependent variables.

Question 33

In stepwise regression procedure,if two independent variables are highly correlated,then:

A) both variables will enter the equation.
B) only one variable will enter the equation.
C) neither variable will enter the equation.
D) None of these is correct.

Question 34

The model $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂ + b₃x₁x₂ is referred to as the:

A) first order model with two predictor variables with no interaction.
B) first order model with two predictor variables with interaction.
C) second order model with three predictor variables with no interaction.
D) second order model with three predictor variables with interaction.

Question 35

In backward selection stepwise regression with ten predictor variables,which of the following statements is correct?

A) The procedure starts with 10 predictor variables and eliminate one predictor at each iteration.
B) The procedure starts with 2 predictor variables and add one predictor at each iteration.
C) The procedure starts with 1 predictor variables and add one predictor at each iteration.
D) The procedure starts with no predictor variables and add one predictor at each iteration.

Question 36

Suppose that the estimated regression equation of a College of Business graduates is given by: $\hat{ Y }$ = 20,000 + 2000x + 1500D,where y is the starting salary,x is the grade point average and D is a dummy variable which takes the value of 1 if the student is a finance major and 0 if not.A hotel management major graduate with a 3.5 grade point average would have an average starting salary of:

A) $22,000.
B) $27,000.
C) $28,500.
D) $20,000.

Question 37

In explaining the amount of money spent on children's toys each year,which of the following independent variables is best represented with a dummy variable?

A) Age
B) Height
C) Gender
D) Weight

Question 38

Stepwise regression is an iterative procedure that:

A) adds one independent variable at a time.
B) deletes one independent variable at a time.
C) adds one dependent variable at a time.
D) deletes one dependent variable at a time.
E) Both A and B are correct.

Question 39

Stepwise regression is especially useful when there are:

A) a great many independent variables.
B) few independent variables.
C) a great many dependent variables.
D) few dependent variables.

Question 40

Which of the following statements are important steps in selecting a model?

A) Specify the dependent variable and determine the goal for the analysis.
B) Specify possible predictor variables and collect the data.
C) Specify the candidate models,and for each candidate model decide which of the available predictor variables will be included in the model.
D) Select a model,evaluate its suitability and test its reliability.
E) All of these.

Question 41

As the temperature increases,an experimental lubricant initially decreases in viscosity (resistance in flow),then increases,then decreases again.Of the first,second,and third polynomial models discussed in this section,which would tend to be most applicable for such data?
What would be the signs of the partial regression coefficient(s)in the model?

Question 42

A researcher suspects that the dependent variable y is linearly related to both x₁ and x₂ but believes there is a little or no interaction between the two predictor variables.Which model would likely be most suitable for this situation?

Question 43

NARRBEGIN: Economist
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction A random sample of 20 daily observations was taken.The computer output is shown below.
Interpret the coefficient b₁.
b₁ = ____________________
Interpretation:

Question 44

The estimated regression equation for a sample of 500 college professors is given by: = 275 - 3x - 2D,where y is retirement age,x is pre-retirement annual income (in $1000s),and D is a dummy variable that takes the value of 0 for female professors and 1 for male professors.Assume that there is a relationship between y,x and D.What is the average age of retirement for male professors with pre-retirement income of $68,500?
____________________ years

Question 45

The ____________________ indicates the proportion of variation in the dependent variable that is "explained" by the set of predictor variables.

Question 46

Suppose that the sample regression equation of a second-order model is given by: = 2.50 + 0.15x + 0.45x² What is the predicted value of y when x = 2?

Question 47

For underlying relationships that are not linear,____________________ transformation methods can be employed in constructing exponential and multiplicative models.

Question 48

Suppose that the sample regression equation of a second-order model is given by: = 2.50 + 0.15x + 0.45x².What does the value 2.50 represent?

Question 49

NARRBEGIN: Economist
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction A random sample of 20 daily observations was taken.The computer output is shown below.
Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: _______________________
Interpretation: __________________________________________________

Question 50

The regression model = 180 + 6x₁ - 2x₂ has been fitted to a set of data.If x₂ = 10,what will be the effect on if x₁ increases by 1 unit? will ____________________ by ____________________

Question 51

In the general polynomial model, the order of the polynomial is:

Question 52

The regression model = 160 + 8x₁ - 5x₂ has been fitted to a set of data.If x₂ = 10,what will be the effect on if x₁ increases by 1 unit? will ____________________ by ____________________

Question 53

The ____________________ method involves forward selection or reverse elimination of one predictor variable at a time.

Question 54

The estimated regression equation for a sample of 500 college professors is given by: = 275 - 3x - 2D,where y is retirement age,x is pre-retirement annual income (in $1000s),and D is a dummy variable that takes the value of 0 for female professors and 1 for male professors.Assume that there is a relationship between y,x and D.What is the average age of retirement for female professors with pre-retirement income of $68,500?
____________________ years

Question 55

NARRBEGIN: Economist
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction A random sample of 20 daily observations was taken.The computer output is shown below.
Is there sufficient evidence at the 1% significance level to conclude that the price of a barrel of oil and the price of gold are linearly related?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: ____________________
Interpretation: _______________________________________________________

Question 56

The regression model = 160 + 8x₁ - 5x₂ has been fitted to a set of data.Comment on whether interaction would appear to exist between x₁ and x₂?
Interaction: ____________________
Comments:

Question 57

NARRBEGIN: Economist
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction A random sample of 20 daily observations was taken.The computer output is shown below.
Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of gold are linearly related?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: _____________________
Interpretation: _____________________________________________________

Question 58

The regression model = 160 + 8x₁ - 5x₂ has been fitted to a set of data.If x₂ = 20,what will be the effect on if x₁ increases by 1 unit? will ____________________ by ____________________

Question 59

NARRBEGIN: Economist
An economist is in the process of developing a model to predict the price of gold.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction A random sample of 20 daily observations was taken.The computer output is shown below.
Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of gold?
Test statistic = ____________________ = ____________________
Critical Value = ____________________
Conclusion: _________________________________
Interpretation: ______________________________________________________

Question 60

If the goal for the regression analysis is simply to predict the value of the dependent variable based on a set of predictor variables,we need not worry about ____________________,which means that some of the predictor variables might be highly correlated with each other.

Question 61

Regression analysis results in the estimation equation log = 3.0 + 0.50 log x₁ + 0.35 log x₂ following data transformation.Transform this equation to the equivalent exponential model of the form = .(The base of the logarithm is 10.) = ____________________

Question 62

As x increases,y increases,but at a decreasing rate.If a second-order polynomial model were fitted to the scatter plot of the data,what would be the signs of the partial regression coefficients in the model?

Question 63

What is stepwise regression,and when is it desirable to make use of this multiple regression technique?

Question 64

After data transformation,regression analysis results in the estimation equation: log = -0.25 + 0.15x.Transform this equation to the equivalent exponential model of the form = b₀b₁^x.(The base of the logarithm is 10.) = ____________________

Question 65

In general,on what basis are independent variables selected for entry into the equation during stepwise regression?

Question 66

What is a correlation matrix,and what role does it play in multiple regression?

Question 67

How do we identify multicollinearity?

Question 68

How do we test the reliability of a model?

Question 69

Briefly discuss the best subset regression approach.

Question 70

Discuss some of the signals for the presence of multicollinearity.

Question 71

A scatter diagram for a set of data shows that as x increases,y initially increases,then it decreases,and then it increases again.What does the scatter diagram indicate?

Question 72

Write a formula for the fourth-order polynomial model.Would such a polynomial model tend to be practical for use with business data?

Question 73

Three predictor variables are being considered for use in a linear regression model.Given the correlation matrix below,does it appear that multicollinearity could be a problem?

Question 74

For a sample of 200 recent credit-card customers of a company's on-line store,the following data are available: the dollar amount of merchandise ordered during the visit,how much time (minutes)the customer spent at the site during the purchase visit,and whether the customer used a Visa,Master Card,or other.Describe the format of a linear regression equation for estimating the dollar amount of the order on the basis of the other variables described above.If any qualitative variables are used,indicate the strategy for coding them.

Question 75

The regression model = 180 + 6x₁ - 2x₂ has been fitted to a set of data.If x₂ = 20,what will be the effect on if x₁ increases by 1 unit? will ____________________ by ____________________

Question 76

As x increases,y decreases,and at an increasing rate.If a second-order polynomial model were fitted to the scatterplot of the data,what would be the signs of the partial regression coefficients in the model?

Question 77

The estimated regression equation for a sample of 500 college professors is given by: = 275 - 3x - 2D,where y is retirement age,x is pre-retirement annual income (in $1000s),and D is a dummy variable that takes the value of 0 for female professors and 1 for male professors.Assume that there is a relationship between y,x and D.How does the average age at retirement for male professors change for each additional thousand dollars of pre-retirement income?
The average age at retirement ____________________ by ____________________ years

Question 78

The two largest values in a correlation matrix are the 0.89 correlation between y and x₃ and the 0.83 correlation between y and x₇.During a stepwise regression analysis is the first independent variable brought into the equation.Will x₇ necessarily be next? If not,why not?

Question 79

What is multicollinearity?

Question 80

The regression model = 180 + 6x₁ - 2x₂ has been fitted to a set of data.Comment on whether interaction appears to exist between x₁ and x₂.
Interaction: _________________________________
Comments: