Question 1

The adjusted multiple coefficient of determination is adjusted for the

Accepted Answer

A)  number of dependent variables. 
B)  number of independent variables. 
C)  number of equations. 
D)  sample size. 
A)  number of dependent variables. 
B)  number of independent variables. 
C)  number of equations. 
D)  sample size.

Question 2

The mathematical equation which has the form of E(y) = β0 + β1x1 + β2x2 + ...+ βpxp relating the expected value of the dependent variable to the value of the independent variables is

Accepted Answer

A)  an estimated multiple nonlinear regression equation. 
B)  a multiple nonlinear regression model. 
C)  an estimated multiple regression equation. 
D)  a multiple regression equation. 
A)  an estimated multiple nonlinear regression equation. 
B)  a multiple nonlinear regression model. 
C)  an estimated multiple regression equation. 
D)  a multiple regression equation.

Question 3

In regression analysis, the response variable is the

Accepted Answer

A)  independent variable. 
B)  dependent variable. 
C)  slope of the regression function. 
D)  intercept. 
A)  independent variable. 
B)  dependent variable. 
C)  slope of the regression function. 
D)  intercept.

Question 4

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}
\begin{array} { l l } 
\text { Coefficients } & \text { Standard Error } \
12.924 & 4.425 \
- 3.682 & 2.630 \
45.216 & 12.560
\end{array}\
\text { Analysis of Variance }\
\begin{array} { l l l l l } 
\text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \
\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }
\end{array} \quad F
\end{array}$$ 
 Carry out the test of significance for the parameter $\beta$1 at the 1% level.The null hypothesis should

Accepted Answer

A)  be rejected. 
B)  not be rejected. 
C)  be revised to test using F statistic. 
D)  be tested for ?? instead. 
A)  be rejected. 
B)  not be rejected. 
C)  be revised to test using F statistic. 
D)  be tested for ?? instead.

Question 5

A term used to describe the case when the independent variables in a multiple regression model are correlated is

Accepted Answer

A)  regression. 
B)  correlation. 
C)  multicollinearity. 
D)  leverage. 
A)  regression. 
B)  correlation. 
C)  multicollinearity. 
D)  leverage.

Question 6

A regression model relating the yearly income (y), age (x1), and the gender of the faculty member of a university (x2 = 1 if female and 0 if male) resulted in the following information. $\hat { y }$ = 5000 + 1.2x1 + .9x2 $\begin{array} { l l l } 
n = 20 & \mathrm { SSE } = 500 & \mathrm { SSR } = 1500 \
s b 1 = .20 & s b _ { 2 } = .10 &
\end{array}$ ​ 
a.
Is gender a significant variable? Let α = .05.
b.
Determine the multiple coefficient of determination.

Accepted Answer

​
a.
t = 9 > critica

Question 7

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.
 $\hat { y }$ = 29 + 18x1 + 43x2 + 87x3
 
For this model, SSR = 600 and SSE = 400.MSR for this model is

Accepted Answer

A)  200. 
B)  10. 
C)  1000. 
D)  43. 
A)  200. 
B)  10. 
C)  1000. 
D)  43.

Question 8

The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x1 in thousands of dollars), and number of salespeople (x2) for a corporation: $$\begin{array}{l}
\text { ANOVA }\
\begin{array} { l l l l l } 
\text { Source } & d f & S S & M S & F \
\text { Regression } & 2 & 822.088 & \
\text { Error } & 7 & 736.012 &
\end{array}
\end{array}$$ ​ 
a.
At α = .05, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
b.
Determine the multiple coefficient of determination.
c.
Determine the adjusted multiple coefficient of determination.
d.
What has been the sample size for this regression analysis?

Accepted Answer

​
a.
F = 3.91 < 4.74; p-value

Question 9

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). $\hat { y }$ = 30 + .7x1 + 3x2
 
Also provided are SST = 1200 and SSE = 384.The yearly income (in $) expected of a 24-year-old female individual is

Accepted Answer

A)  $19.80. 
B)  $19,800. 
C)  $49.80. 
D)  $49,800. 
A)  $19.80. 
B)  $19,800. 
C)  $49.80. 
D)  $49,800.

Question 10

A multiple regression was performed on a sample of 16 observations.The estimated equation is $\hat { y }$ = 23.5 - 14.28x1 + 6.72x2 + 15.68x3.The standard errors for the coefficients are sb1 = 4.2, sb2 = 5.6, and sb3 = 2.8.For this model, SST = 3809.6 and SSR = 3285.4.
​ 
a.
Compute the appropriate t ratios.
b.
Test for the significance of β1, β2, and β3 at the 5% level of significance.
c.
Do you think any of the variables should be dropped from the model? Explain.
d.
Compute R2 and $R _ { \mathrm { a } } ^ { 2 }$ . Interpret R2. 
e.
Test the significance of the relationship among the variables at the 5% level of significance.

Accepted Answer

a. t₁ = -3.4, t₂ = 1.2, t₃ = 5.6 b. t_.025 = 2

Question 11

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.
 $\hat { y }$ = 29 + 18x1 + 43x2 + 87x3
 
For this model, SSR = 600 and SSE = 400.The computed F statistic for testing the significance of the above model is

Accepted Answer

A)  1.50. 
B)  20.00. 
C)  .600. 
D)  .667. 
A)  1.50. 
B)  20.00. 
C)  .600. 
D)  .667.

Question 12

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40.The multiple coefficient of determination is

Accepted Answer

A)  .80. 
B)  .90. 
C)  .25. 
D)  .15. 
A)  .80. 
B)  .90. 
C)  .25. 
D)  .15.

Question 13

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. ANOVA
$\begin{array} { l l l l l l } & d f & S S & M S & F \ 
\text { Regression } &\_\_\_ ?&\_\_\_ ?&\_\_\_ ?&\_\_\_ ?\
 \text {Error (Residual) }&\_\_\_ ? &\_\_\_ ?&30\
\hline\text {Total }&&990\
 \end{array}$ ​
Fill in all the blanks in the above ANOVA table.

Accepted Answer

The answer of In a regression analysis involving 20 observations...

Question 14

A regression model in which more than one independent variable is used to predict the dependent variable is called

Accepted Answer

A)  a simple linear regression model. 
B)  a multiple regression model. 
C)  an independent model. 
D)  an adjusted prediction model. 
A)  a simple linear regression model. 
B)  a multiple regression model. 
C)  an independent model. 
D)  an adjusted prediction model.

Question 15

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}
\begin{array} { l l } 
\text { Coefficients } & \text { Standard Error } \
12.924 & 4.425 \
- 3.682 & 2.630 \
45.216 & 12.560
\end{array}\
\text { Analysis of Variance }\
\begin{array} { l l l l l } 
\text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \
\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }
\end{array} \quad F
\end{array}$$ 
 The sum of squares due to error (SSE) equals

Accepted Answer

A)  373.31. 
B)  485.3. 
C)  4853. 
D)  6308.9. 
A)  373.31. 
B)  485.3. 
C)  4853. 
D)  6308.9.

Question 16

The equation which has the form of E(y) = $\hat { y }$ = b0 + b1x1 + b2x2 + ...+ bpxp is

Accepted Answer

A)  an estimated multiple nonlinear regression equation. 
B)  a multiple nonlinear regression model. 
C)  an estimated multiple regression equation. 
D)  a multiple regression equation. 
A)  an estimated multiple nonlinear regression equation. 
B)  a multiple nonlinear regression model. 
C)  an estimated multiple regression equation. 
D)  a multiple regression equation.

Question 17

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier.This difficulty can be circumvented by using​

Accepted Answer

A)  categorical independent variables. 
B)  ​residual transformation. 
C)  ​studentized deleted residuals. 
D)  ​logistic regression. 
A)  categorical independent variables. 
B)  ​residual transformation. 
C)  ​studentized deleted residuals. 
D)  ​logistic regression.

Question 18

Below you are given a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (y), unit price (x1 in $1000), and the number of advertising spots (x2) they used on a local television station. $$\begin{array}{l}
\text { ANOVA }\
\begin{array} { l l l l l l } 
& d f & \text { SS } & M S & F & \text { Significance } F \
\text { Regression } & 2 & 655.955 & & & \
\text { Residual } & 9 & & &
\end{array}
\end{array}$$ ​ 
a.
At α = .05, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
b.
Determine the multiple coefficient of determination.
c.
Determine the adjusted multiple coefficient of determination.

Accepted Answer

​
a.
F = 16.13; p-va

Question 19

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $$\begin{array}{l}
\begin{array} { l l } 
\text { Coefficients } & \text { Standard Error } \
12.924 & 4.425 \
- 3.682 & 2.630 \
45.216 & 12.560
\end{array}\
\text { Analysis of Variance }\
\begin{array} { l l l l l } 
\text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \
\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }
\end{array} \quad F
\end{array}$$ 
 The degrees of freedom for the sum of squares explained by the regression (SSR) are

Accepted Answer

A)  2. 
B)  3. 
C)  13. 
D)  15. 
A)  2. 
B)  3. 
C)  13. 
D)  15.

Question 20

In multiple regression analysis,

Accepted Answer

A)  there can be any number of dependent variables, but only one independent variable. 
B)  the adjusted coefficient of determination can never be negative. 
C)  the multiple coefficient of determination must be larger than 1. 
D)  there can be several independent variables, but only one dependent variable. 
A)  there can be any number of dependent variables, but only one independent variable. 
B)  the adjusted coefficient of determination can never be negative. 
C)  the multiple coefficient of determination must be larger than 1. 
D)  there can be several independent variables, but only one dependent variable.

The adjusted multiple coefficient of determination is adjusted for the

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ...+ β_pxp relating the expected value of the dependent variable to the value of the independent variables is

In regression analysis, the response variable is the

A term used to describe the case when the independent variables in a multiple regression model are correlated is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃ For this model, SSR = 600 and SSE = 400.MSR for this model is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃ For this model, SSR = 600 and SSE = 400.The computed F statistic for testing the significance of the above model is

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40.The multiple coefficient of determination is

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. ANOVA df SS MS F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error (Residual) \_\_\_? \_\_\_? 30 Total 990 Fill in all the blanks in the above ANOVA table.

A regression model in which more than one independent variable is used to predict the dependent variable is called

The equation which has the form of E(y) = $\hat { y }$ = b₀ + b₁x₁ + b₂x₂ + ...+ b_px_p is

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier.This difficulty can be circumvented by using

In multiple regression analysis,

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Filters

Exam 15: Multiple Regression

The adjusted multiple coefficient of determination is adjusted for the

The mathematical equation which has the form of E(y) = β0 + β1x1 + β2x2 + ...+ βpxp relating the expected value of the dependent variable to the value of the independent variables is

In regression analysis, the response variable is the

A term used to describe the case when the independent variables in a multiple regression model are correlated is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. y^\hat { y }y^​ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400.MSR for this model is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. y^\hat { y }y^​ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400.The computed F statistic for testing the significance of the above model is

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40.The multiple coefficient of determination is

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. ANOVA df SS MS F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error (Residual) \_\_\_? \_\_\_? 30 Total 990 ​ Fill in all the blanks in the above ANOVA table.

A regression model in which more than one independent variable is used to predict the dependent variable is called

The equation which has the form of E(y) = y^\hat { y }y^​ = b0 + b1x1 + b2x2 + ...+ bpxp is

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier.This difficulty can be circumvented by using​

In multiple regression analysis,

Data and Statistics

Descriptive Statistics: Tabulargraphical

Descriptive Statistics: Numerical

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Filters

The mathematical equation which has the form of E(y) = β₀ + β₁x₁ + β₂x₂ + ...+ β_pxp relating the expected value of the dependent variable to the value of the independent variables is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃ For this model, SSR = 600 and SSE = 400.MSR for this model is

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. $\hat { y }$ = 29 + 18x₁ + 43x₂ + 87x₃ For this model, SSR = 600 and SSE = 400.The computed F statistic for testing the significance of the above model is

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. ANOVA df SS MS F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error (Residual) \_\_\_? \_\_\_? 30 Total 990 Fill in all the blanks in the above ANOVA table.

The equation which has the form of E(y) = $\hat { y }$ = b₀ + b₁x₁ + b₂x₂ + ...+ b_px_p is

Even though a residual may be unusually large, the standardized residual rule might fail to identify the observation as being an outlier.This difficulty can be circumvented by using