Question 1

A dummy variable will have a value of either ____________________ or ____________________,depending on whether a given characteristic is present or absent.

Accepted Answer

The answer of A dummy variable will have a value...

Question 2

A multiple regression model has three independent variables.The following values of y are given: 
$\begin{array}{llcc}
42&40&40&70&52&28&55&48&60&50
\end{array}$ Compute the total sum of squares (SST).
SST = ____________________

Accepted Answer

The answer of A multiple regression model has three independent...

Question 3

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex What is the estimated weight loss of a female who stayed in the program for 5 time periods?

Accepted Answer

The answer of A health science-kinesiology program to lose weight...

Question 4

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

Accepted Answer

The answer of Consider the multiple regression equation, \(\hat {...

Question 5

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

Accepted Answer

The answer of For a multiple regression model the following...

Question 6

In a regression model involving 50 observations,the following estimated regression model was obtained. $\hat { Y }$ = 51.4 + 0.70x₁ + 0.679x₂ - 0.378x₃.For this model SST = 120,524 and SSR = 85,400.Then,the value of MSE is:

Accepted Answer

MSE (Mean Squared Error) is calculated as SSE/(n-k-1), where SSE = SST - SSR. Here, SSE = 120,524 - 85,400 = 35,124. With n = 50 and k = 3, MSE = 35,124 / (50 - 3 - 1) = 763.565.

Question 7

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

Accepted Answer

The null hypothesis for testing the significance of a multiple regression model is that all the regression coefficients (β's) are equal to 0, which means that none of the independent variables have a significant effect on the dependent variable. Therefore, the correct null hypothesis in this case is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$. Choice A and B are incorrect because they assume that the regression coefficients are equal to 1, which may not be the case. Choice D is also incorrect because it assumes that the coefficients are not equal to 0, which is not the null hypothesis for testing the significance of the model.

Question 8

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

Accepted Answer

The answer of With four or more variables,the regression equation...

Question 9

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

Accepted Answer

The answer of In a multiple regression problem,the regression equation...

Question 10

States
Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables:
xS1U1B11S1U1B0 = Police per 10,000 persons,by state
xS1U1B12S1U1B0 = Expenditure by local government for police protection,in thousands,by state
xS1U1B13S1U1B0 = New passenger car registrations,in thousands,by state.
Data from 13 states were collected.The MINITAB regression results are: 
The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \text { R-sq } = ? ? \% \quad \text { R-sq(adj) } = ? ? \%$$
$\begin{array}{l}
\text { Analysis of Variance }\
\begin{array} { l l l l c l } 
\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \
\text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \
\text { Error } & 9 & 924 & 103 & & \
\text { Total } & 12 & 33932 & & &
\end{array}
\end{array}$
$\begin{array}{l}
\text { Correlation between the variables: }\
\begin{array} { l r c c c } 
& \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \
\text { car-thf } & 1.000 & & & \
\text { police } & 0.466 & 1.000 & & \
\text { polexp } & 0.970 & 0.390 & 1.000 & \
\text { registr } & 0.976 & 0.406 & 0.958 & 1.000
\end{array}
\end{array}$
-How much of the variation in thefts is explained by the model?

Accepted Answer

The answer of States
Concern over the number of car thefts...

Question 11

States Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables: xS1U1B11S1U1B0 = Police per 10,000 persons,by state xS1U1B12S1U1B0 = Expenditure by local government for police protection,in thousands,by state xS1U1B13S1U1B0 = New passenger car registrations,in thousands,by state. Data from 13 states were collected.The MINITAB regression results are: The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr $\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$ $$s = ? ? \quad \text { R-sq } = ? ? \% \quad \text { R-sq(adj) } = ? ? \%$$ $\begin{array}{l} \text { Analysis of Variance }\ \begin{array} { l l l l c l } \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \ \text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \ \text { Error } & 9 & 924 & 103 & & \ \text { Total } & 12 & 33932 & & & \end{array} \end{array}$ $\begin{array}{l} \text { Correlation between the variables: }\ \begin{array} { l r c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \ \text { car-thf } & 1.000 & & & \ \text { police } & 0.466 & 1.000 & & \ \text { polexp } & 0.970 & 0.390 & 1.000 & \ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array} \end{array}$ -Compute the multiple standard error of estimate (s_e)from the regression results.

Accepted Answer

The answer of States
Concern over the number of car thefts...

Question 12

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

Accepted Answer

The answer of In a regression model involving 25 observations,the...

Question 13

In a multiple regression analysis involving k independent variables and n data points,the degrees of freedom associated with the error sum of squares is:

Accepted Answer

In multiple regression analysis, the degrees of freedom associated with the error sum of squares is n - k - 1, where n is the number of data points and k is the number of independent variables. This is because we lose one degree of freedom for each independent variable included in the model, as well as one additional degree of freedom for the intercept term. Therefore, we have to subtract k + 1 from the total sample size to arrive at the degrees of freedom associated with the error sum of squares.

Question 14

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex.For the same length of time in the program,compare the weight loss of a female to a male.What is your conclusion?

Accepted Answer

The answer of A health science-kinesiology program to lose weight...

Question 15

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$= 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

Accepted Answer

MSR (Mean Square Regression) is calculated as SSR divided by the degrees of freedom for the regression, which is the number of independent variables. In this model, there are 3 independent variables (x1, x2, x3), so the degrees of freedom for the regression is 3. Thus, MSR = SSR / degrees of freedom for regression = 300 / 3 = 100.

Question 16

A health science-kinesiology program to lose weight collected data from ten students.Sex was coded as 1 = female and 0 = male.The regression equation obtained was given by: Pounds lost = 15.8 + 0.65 time + 6.00 sex.What is the estimated weight loss of a male who stayed in the program for 5 time periods?

Accepted Answer

The answer of A health science-kinesiology program to lose weight...

Question 17

The ____________________ is the proportion of the variation in y that is explained by the multiple regression equation.

Accepted Answer

The answer of The ____________________ is the proportion of the...

Question 18

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively)for the critical value of F are:

Accepted Answer

The numerator degrees of freedom for the F-test in multiple regression is equal to the number of independent variables, which is 4. The denominator degrees of freedom is calculated as the total number of observations minus the number of independent variables minus 1 (30 - 4 - 1 = 25).

Question 19

Motor Vehicle In order to predict motor vehicle purchases for the U.S.,the coefficients of a multiple regression equation were estimated using 25 years of data.The variables were: y = motor vehicle purchases (billions of dollars) xS1U1B11S1U1B0 = disposable personal income (billions of dollars) xS1U1B12S1U1B0 = U.S.population (millions of persons) xS1U1B13S1U1B0 = automobile installment credit (billions of dollars) Part of the results using MINITAB was: The regression equation is $Y = - 61.3 - 0.0022 \times 1 + 0.368 \times 2 + 0.725 \times 3$ $\begin{array} { l l l l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } \ \text { Constant } & - 61.28 & 36.96 & - 1.66 \ \text { X1 } & - 0.00221 & 0.01504 & - 0.15 \ \text { X2 } & 0.3679 & 0.2001 & 1.84 \ \text { X3 } & 0.7254 & 0.2115 & 3.43 \end{array}$ Analysis of Variance $\begin{array} { l c l } \text { SOURCE } & \text { DF } & \text { SS } \ \text { Regression } & 3 & 32624 \ \text { Error } & 21 & 591 \ \text { Total } & 24 & 33215 \end{array}$ -Use the values in the analysis of variance table to compute R² using the values for SST and SSE or SSR.

Accepted Answer

The answer of Motor Vehicle
In order to predict motor vehicle...

Question 20

Motor Vehicle
In order to predict motor vehicle purchases for the U.S.,the coefficients of a multiple regression equation were estimated using 25 years of data.The variables were:
y = motor vehicle purchases (billions of dollars)
xS1U1B11S1U1B0 = disposable personal income (billions of dollars)
xS1U1B12S1U1B0 = U.S.population (millions of persons)
xS1U1B13S1U1B0 = automobile installment credit (billions of dollars)
Part of the results using MINITAB was: The regression equation is
$Y = - 61.3 - 0.0022 \times 1 + 0.368 \times 2 + 0.725 \times 3$
$\begin{array} { l l l l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } \ \text { Constant } & - 61.28 & 36.96 & - 1.66 \ \text { X1 } & - 0.00221 & 0.01504 & - 0.15 \ \text { X2 } & 0.3679 & 0.2001 & 1.84 \ \text { X3 } & 0.7254 & 0.2115 & 3.43 \end{array}$
Analysis of Variance
$\begin{array} { l c l } \text { SOURCE } & \text { DF } & \text { SS } \ \text { Regression } & 3 & 32624 \ \text { Error } & 21 & 591 \ \text { Total } & 24 & 33215 \end{array}$
-Use the values in the analysis of variance table to compute the multiple standard error of the estimate.

Accepted Answer

The answer of Motor Vehicle
In order to predict motor vehicle...

Quiz 16: Multiple Regression and Correlation

A dummy variable will have a value of either or ,depending on whether a given characteristic is present or absent.

A multiple regression model has three independent variables.The following values of y are given: $\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}$ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

In a regression model involving 50 observations,the following estimated regression model was obtained. $\hat { Y }$ = 51.4 + 0.70x₁ + 0.679x₂ - 0.378x₃.For this model SST = 120,524 and SSR = 85,400.Then,the value of MSE is:

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a multiple regression analysis involving k independent variables and n data points,the degrees of freedom associated with the error sum of squares is:

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

The ____________________ is the proportion of the variation in y that is explained by the multiple regression equation.

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively) for the critical value of F are:

Quiz 16: Multiple Regression and Correlation

A dummy variable will have a value of either ____________________ or ____________________,depending on whether a given characteristic is present or absent.

A multiple regression model has three independent variables.The following values of y are given: 42404070522855486050\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}42​40​40​70​52​28​55​48​60​50​ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, Y^\hat { Y }Y^ = 80 + 15x1 - 5 x2 + 100x3.If x1 = 10,x2 = 4,x3 = 12,what is the estimated value of y?

For a multiple regression model the following statistics are given: SSE = 40,SST = 200,k = 4,n = 20.Calculate the coefficient of determination adjusted for degrees of freedom.

In a regression model involving 50 observations,the following estimated regression model was obtained. Y^\hat { Y }Y^ = 51.4 + 0.70x1 + 0.679x2 - 0.378x3.For this model SST = 120,524 and SSR = 85,400.Then,the value of MSE is:

In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:

With four or more variables,the regression equation becomes a mathematical entity called a ____________________.

In a multiple regression problem,the regression equation is given by Y^\hat { Y }Y^ = 58.0 - 5.66x1 + 0.61 x2.Compute the point estimate for y when x1 = 3 and x2 = 4.

In a regression model involving 25 observations,the following estimated regression model was obtained: Y^\hat { Y }Y^ = 60 + 2.8x1 + 1.2x2 - x3.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a multiple regression analysis involving k independent variables and n data points,the degrees of freedom associated with the error sum of squares is:

In a regression model involving 40 observations, the following estimated regression model was obtained y^\hat{y}y^​ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is:

The ____________________ is the proportion of the variation in y that is explained by the multiple regression equation.

In order to test the significance of a multiple regression model involving 4 independent variables and 30 observations,the numerator and denominator degrees of freedom (respectively) for the critical value of F are:

A dummy variable will have a value of either or ,depending on whether a given characteristic is present or absent.

A multiple regression model has three independent variables.The following values of y are given: $\begin{array}{llcc}42&40&40&70&52&28&55&48&60&50\end{array}$ Compute the total sum of squares (SST). SST = ____________________

Consider the multiple regression equation, $\hat { Y }$ = 80 + 15x₁ - 5 x₂ + 100x₃.If x₁ = 10,x₂ = 4,x₃ = 12,what is the estimated value of y?

In a regression model involving 50 observations,the following estimated regression model was obtained. $\hat { Y }$ = 51.4 + 0.70x₁ + 0.679x₂ - 0.378x₃.For this model SST = 120,524 and SSR = 85,400.Then,the value of MSE is:

In a multiple regression problem,the regression equation is given by $\hat { Y }$ = 58.0 - 5.66x₁ + 0.61 x₂.Compute the point estimate for y when x₁ = 3 and x₂ = 4.

In a regression model involving 25 observations,the following estimated regression model was obtained: $\hat { Y }$ = 60 + 2.8x₁ + 1.2x₂ - x₃.For this model,SST = 600 and SSE = 150.Calculate the value of the F statistic for testing the significance of this model. F = ____________________

In a regression model involving 40 observations, the following estimated regression model was obtained $\hat{y}$ = 10 + 3x1 + 5x2 + 6x3. For this model, SSR = 300 and SSE = 75. Then, the value of MSR is: