Question 1

Which of the following statements regarding multicollinearity is not true?

Accepted Answer

A) It exists in virtually all multiple regression models. 
B) It is also called collinearity and intercorrelation. 
C) It is a condition that exists when the independent variables are highly correlated with the dependent variable. 
D) All of these choices are true. 
A) It exists in virtually all multiple regression models. 
B) It is also called collinearity and intercorrelation. 
C) It is a condition that exists when the independent variables are highly correlated with the dependent variable. 
D) All of these choices are true. C

Question 2

When an explanatory variable is dropped from a multiple regression model, the adjusted coefficient of determination can increase.

Accepted Answer

A) True 
 B)False  True

Question 3

In a multiple regression model, the probability distribution of the error variable $\varepsilon$ is assumed to be:

Accepted Answer

A) normal. 
B) non-normal. 
C) positively skewed. 
D) negatively skewed. 
A) normal. 
B) non-normal. 
C) positively skewed. 
D) negatively skewed. A

Question 4

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81. The percentage of the variation in y that is explained by the regression equation is:

Accepted Answer

A) 81% 
B) 90% 
C) 86% 
D) about 16% 
A) 81% 
B) 90% 
C) 86% 
D) about 16%

Question 5

NARRBEGIN: Real Estate Builder
Real Estate Builder
A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below.SUMMARY OUTPUT
 $$\begin{array}{l}
\text { Regression Statistics }\
\begin{array} { l l } 
\text { Multiple R } & 0.865 \
\text { R. Square} & 0.748 \
\text { Adjusted R Square } & 0.726 \
\text {Standard Error } & 5.195 \
\text { Observations } & 50
\end{array}
\end{array}$$ ANOVA
 $\begin{array}{l|ccccc} 
& d f & \text { SS } & M S & F & \text { Signif F } \
\hline \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & \
\text { Total } & 49 & 4820.0000 & &
\end{array}$ $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { st.error } & \boldsymbol { t }\boldsymbol { state } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .798 \
\text { Family Income } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$ NARREND
-{Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually: $\alpha$ = .01, .05, .10, or .15?

Accepted Answer

The answer of NARRBEGIN: Real Estate Builder
Real Estate Builder
A real...

Question 6

NARRBEGIN: Real Estate Builder
Real Estate Builder
A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below.SUMMARY OUTPUT
 $$\begin{array}{l}
\text { Regression Statistics }\
\begin{array} { l l } 
\text { Multiple R } & 0.865 \
\text { R. Square} & 0.748 \
\text { Adjusted R Square } & 0.726 \
\text {Standard Error } & 5.195 \
\text { Observations } & 50
\end{array}
\end{array}$$ ANOVA
 $\begin{array}{l|ccccc} 
& d f & \text { SS } & M S & F & \text { Signif F } \
\hline \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & \
\text { Total } & 49 & 4820.0000 & &
\end{array}$ $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { st.error } & \boldsymbol { t }\boldsymbol { state } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .798 \
\text { Family Income } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$ NARREND
-{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on income is significantly different from 0. What is the value of the relevant t-statistic?

Accepted Answer

The answer of NARRBEGIN: Real Estate Builder
Real Estate Builder
A real...

Question 7

If the value of the Durbin-Watson statistic d is large (d > 2), this indicates a(n) ____________________ (positive/negative) first-order autocorrelation exists.

Accepted Answer

The answer of If the value of the Durbin-Watson statistic...

Question 8

NARRBEGIN: Life Expectancy
Life Expectancy
An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week (xS1U1B11S1U1B0), the cholesterol level (xS1U1B12S1U1B0), and the number of points that the individual's blood pressure exceeded the recommended value (xS1U1B13S1U1B0). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below.THE REGRESSION EQUATION IS
y = 55.8 + 1.79xS1U1B11S1U1B0 - 0.021xS1U1B12S1U1B0 -0.061xS1U1B13S1U1B0
 $$\begin{array} { | c | c c c | } 
\hline \text { predictor } & Coef  & SUDev  & T \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
\boldsymbol { \lambda } _ { 1 } & 1.79 & 0.44 & 4.068 \
\lambda _ { 2 } & - 0.021 & 0.011 & - 1.909 \
\lambda _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ $$S = 9.47 \quad R - S q = 22.5 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { d } & \mathbf { SS } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Tatol } & 39 & 4166 & & \
\hline
\end{array}$$ NARREND
-{Life Expectancy Narrative} What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

R² = 0.225. This means that 22.5% of the

Question 9

NARRBEGIN: Real Estate Builder
Real Estate Builder
A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below.SUMMARY OUTPUT
 $$\begin{array}{l}
\text { Regression Statistics }\
\begin{array} { l l } 
\text { Multiple R } & 0.865 \
\text { R. Square} & 0.748 \
\text { Adjusted R Square } & 0.726 \
\text {Standard Error } & 5.195 \
\text { Observations } & 50
\end{array}
\end{array}$$ ANOVA
 $\begin{array}{l|ccccc} 
& d f & \text { SS } & M S & F & \text { Signif F } \
\hline \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & \
\text { Total } & 49 & 4820.0000 & &
\end{array}$ $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { st.error } & \boldsymbol { t }\boldsymbol { state } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .798 \
\text { Family Income } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$ NARREND
-{Real Estate Builder Narrative} What are the regression degrees of freedom that are missing from the output?

Accepted Answer

df = 3605.

Question 10

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

Accepted Answer

A) 6.26 
B) 3.33 
C) 9.36 
D) 4.24 
A) 6.26 
B) 3.33 
C) 9.36 
D) 4.24

Question 11

NARRBEGIN: Real Estate Builder
Real Estate Builder
A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A partial computer output is shown below.SUMMARY OUTPUT
 $$\begin{array}{l}
\text { Regression Statistics }\
\begin{array} { l l } 
\text { Multiple R } & 0.865 \
\text { R. Square} & 0.748 \
\text { Adjusted R Square } & 0.726 \
\text {Standard Error } & 5.195 \
\text { Observations } & 50
\end{array}
\end{array}$$ ANOVA
 $\begin{array}{l|ccccc} 
& d f & \text { SS } & M S & F & \text { Signif F } \
\hline \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \
\text { Residual } & & 1214.2264 & 26.9828 & \
\text { Total } & 49 & 4820.0000 & &
\end{array}$ $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { st.error } & \boldsymbol { t }\boldsymbol { state } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .798 \
\text { Family Income } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$ NARREND
-{Real Estate Builder Narrative} When the builder used a simple linear regression model with house size as the dependent variable and education as the independent variable, he obtained an R-square value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

Accepted Answer

86.5% -23.0% = 63.5%. This mea

Question 12

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?
 $$\begin{array} { | l | c c c | } 
\hline  & \boldsymbol { x } _ { 1 } & \boldsymbol { x } _ { \mathbf { 1 } } & \boldsymbol { x } _ { \mathbf { 3 } } \
\hline \boldsymbol { x } _ { 1 } & 1.000 & & \
\boldsymbol { x } _ { \mathbf { 2 } } & 0.025 & 1.000 & \
\boldsymbol { x } _ { \mathbf { 3 } } & 0.968 & 0.897 & 1.000 \
\hline
\end{array}$$

Accepted Answer

It appears that multicollinear

Question 13

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

Accepted Answer

A) heteroscedasticity. 
B) homoscedasticity. 
C) multicollinearity. 
D) None of these choices. 
A) heteroscedasticity. 
B) homoscedasticity. 
C) multicollinearity. 
D) None of these choices.

Question 14

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

Accepted Answer

A) True 
 B)False

Question 15

If multicollinearity exists among the independent variables included in a multiple regression model, then:

Accepted Answer

A) the regression coefficients will be difficult to interpret. 
B) the standard errors of the regression coefficients for the correlated independent variables will increase. 
C) one or more of the coefficients may have the wrong sign. 
D) All of these choices are true. 
A) the regression coefficients will be difficult to interpret. 
B) the standard errors of the regression coefficients for the correlated independent variables will increase. 
C) one or more of the coefficients may have the wrong sign. 
D) All of these choices are true.

Question 16

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

Accepted Answer

The answer of One clue to the presence of multicollinearity...

Question 17

____________________ is a condition that exists when independent variables are correlated with one another.

Accepted Answer

The answer of ____________________ is a condition that exists when...

Question 18

Test the hypotheses: H0: There is no first-order autocorrelation vs. H1: There is negative first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.75, n = 20, k = 2, and $\alpha$ = 0.01.

Accepted Answer

d_L = 0.86 and d_U = 1.27 The decision is ma

Question 19

NARRBEGIN: Life Expectancy
Life Expectancy
An actuary wanted to develop a model to predict how long individuals will live. After consulting a number of physicians, she collected the age at death (y), the average number of hours of exercise per week (xS1U1B11S1U1B0), the cholesterol level (xS1U1B12S1U1B0), and the number of points that the individual's blood pressure exceeded the recommended value (xS1U1B13S1U1B0). A random sample of 40 individuals was selected. The computer output of the multiple regression model is shown below.THE REGRESSION EQUATION IS
y = 55.8 + 1.79xS1U1B11S1U1B0 - 0.021xS1U1B12S1U1B0 -0.061xS1U1B13S1U1B0
 $$\begin{array} { | c | c c c | } 
\hline \text { predictor } & Coef  & SUDev  & T \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
\boldsymbol { \lambda } _ { 1 } & 1.79 & 0.44 & 4.068 \
\lambda _ { 2 } & - 0.021 & 0.011 & - 1.909 \
\lambda _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ $$S = 9.47 \quad R - S q = 22.5 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { d } & \mathbf { SS } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repression } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Tatol } & 39 & 4166 & & \
\hline
\end{array}$$ NARREND
-{Life Expectancy Narrative} Interpret the coefficient b1.

Accepted Answer

b₁ = 1.79. This tells us for each additio

Question 20

In reference to the equation $\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the y-intercept.

Accepted Answer

A) True 
 B)False

Which of the following statements regarding multicollinearity is not true?

When an explanatory variable is dropped from a multiple regression model, the adjusted coefficient of determination can increase.

In a multiple regression model, the probability distribution of the error variable $\varepsilon$ is assumed to be:

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81. The percentage of the variation in y that is explained by the regression equation is:

If the value of the Durbin-Watson statistic d is large (d > 2), this indicates a(n) ____________________ (positive/negative) first-order autocorrelation exists.

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

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? 1.000 0.025 1.000 0.968 0.897 1.000

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

If multicollinearity exists among the independent variables included in a multiple regression model, then:

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

____________________ is a condition that exists when independent variables are correlated with one another.

Test the hypotheses: H₀: There is no first-order autocorrelation vs. H₁: There is negative first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.75, n = 20, k = 2, and $\alpha$ = 0.01.

In reference to the equation $\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the y-intercept.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Filters

Exam 17: Multiple Regression

Which of the following statements regarding multicollinearity is not true?

When an explanatory variable is dropped from a multiple regression model, the adjusted coefficient of determination can increase.

In a multiple regression model, the probability distribution of the error variable ε\varepsilonε is assumed to be:

A multiple regression equation includes 5 independent variables, and the coefficient of determination is 0.81. The percentage of the variation in y that is explained by the regression equation is:

If the value of the Durbin-Watson statistic d is large (d > 2), this indicates a(n) ____________________ (positive/negative) first-order autocorrelation exists.

A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:

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? 1.000 0.025 1.000 0.968 0.897 1.000

When the independent variables are correlated with one another in a multiple regression analysis, this condition is called:

From the coefficient of determination, we cannot detect the strength of the relationship between the dependent variable y and any individual independent variable.

If multicollinearity exists among the independent variables included in a multiple regression model, then:

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

____________________ is a condition that exists when independent variables are correlated with one another.

Test the hypotheses: H0: There is no first-order autocorrelation vs. H1: There is negative first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.75, n = 20, k = 2, and α\alphaα = 0.01.

In reference to the equation y^=−0.80+0.12x1+0.08x2\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }y^​=−0.80+0.12x1​+0.08x2​ , the value -0.80 is the y-intercept.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Filters

In a multiple regression model, the probability distribution of the error variable $\varepsilon$ is assumed to be:

Test the hypotheses: H₀: There is no first-order autocorrelation vs. H₁: There is negative first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.75, n = 20, k = 2, and $\alpha$ = 0.01.

In reference to the equation $\hat { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ , the value -0.80 is the y-intercept.