Question 1

For the following multiple regression model: $\hat { y } = 2 - 3 x _ { 1 } + 4 x _ { 2 } + 5 x _ { 3 }$ , a unit increase in x1, holding x2 and x3 constant, results in:

Accepted Answer

A) a decrease of 3 units on average in the value of y. 
B) an increase of 8 units in the value of y. 
C) an increase of 3 units on average in the value of y. 
D) None of these choices. 
A) a decrease of 3 units on average in the value of y. 
B) an increase of 8 units in the value of y. 
C) an increase of 3 units on average in the value of y. 
D) None of these choices.

Question 2

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

Accepted Answer

A) F-test 
B) t-test 
C) z-test 
D) None of these choices. 
A) F-test 
B) t-test 
C) z-test 
D) None of these choices.

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

A high correlation between two independent variables is an indication of ____________________.

Accepted Answer

The answer of A high correlation between two independent variables...

Question 5

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is ____________________ with a mean of ____________________.

Accepted Answer

normal; ze

Question 6

Test the hypotheses H0: There is no first-order autocorrelation vs. H1: There is positive first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.12, n = 45, k = 5, and $\alpha$ = 0.05.

Accepted Answer

d_L = 1.29 and d_U = 1.78 The decision is ma

Question 7

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

Accepted Answer

The answer of If the residuals in a regression analysis...

Question 8

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400. Then, the value of MSE is 560.

Accepted Answer

A) True 
 B)False

Question 9

The total variation in y is equal to SSR + ____________________.

Accepted Answer

SSE
sum of

Question 10

Suppose a multiple regression analysis involving 25 data points has $s _ { z } ^ { 2 } = 1.8$ and SSE = 36. Then, the number of the independent variables must be:

Accepted Answer

A) 3 
B) 4 
C) 5 
D) 6 
A) 3 
B) 4 
C) 5 
D) 6

Question 11

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 b2.

Accepted Answer

b₂ = -0.021. This tells us that for each

Question 12

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 minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home?

Accepted Answer

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

Question 13

The validity of a multiple regression model is tested using a(n) _________ test.

Accepted Answer

The answer of The validity of a multiple regression model...

Question 14

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} At the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of education in the regression model?

Accepted Answer

Education is not significant i

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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} Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

Accepted Answer

@#LAT-DLM& vs. @#LAT-DLM& Rejection region: | t | > t_0.005,36 @#LAT-DLM& 2.724

Question 17

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 numerator and denominator degrees of freedom for the F-statistic?

Accepted Answer

df = 4 for the numer

Question 18

If the value of the Durbin-Watson test statistic, d, satisfies the inequalities d L or d > 4 - dL, where dL and dU are the critical values of d, we conclude that positive first-order autocorrelation exists.

Accepted Answer

A) True 
 B)False

Question 19

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

Accepted Answer

The answer of A practical way to identify multicollinearity is...

Question 20

In a multiple regression model, the following statistics are given: SSE = 100, R2 = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

Accepted Answer

A) 0.930 
B) 0.900 
C) 0.955 
D) 0.855 
A) 0.930 
B) 0.900 
C) 0.955 
D) 0.855

For the following multiple regression model: $\hat { y } = 2 - 3 x _ { 1 } + 4 x _ { 2 } + 5 x _ { 3 }$ , a unit increase in x₁, holding x₂ and x₃ constant, results in:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

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

A high correlation between two independent variables is an indication of ____________________.

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is with a mean of .

Test the hypotheses H₀: There is no first-order autocorrelation vs. H₁: There is positive first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.12, n = 45, k = 5, and $\alpha$ = 0.05.

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400. Then, the value of MSE is 560.

The total variation in y is equal to SSR + ____________________.

Suppose a multiple regression analysis involving 25 data points has $s _ { z } ^ { 2 } = 1.8$ and SSE = 36. Then, the number of the independent variables must be:

The validity of a multiple regression model is tested using a(n) _________ test.

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

If the value of the Durbin-Watson test statistic, d, satisfies the inequalities d < d_L or d > 4 - d_L, where d_L and d_U are the critical values of d, we conclude that positive first-order autocorrelation exists.

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

In a multiple regression model, the following statistics are given: SSE = 100, R² = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

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

For the following multiple regression model: y^=2−3x1+4x2+5x3\hat { y } = 2 - 3 x _ { 1 } + 4 x _ { 2 } + 5 x _ { 3 }y^​=2−3x1​+4x2​+5x3​ , a unit increase in x1, holding x2 and x3 constant, results in:

To test the validity of a multiple regression model, we test the null hypothesis that the regression coefficients are all zero by applying the:

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

A high correlation between two independent variables is an indication of ____________________.

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is ____________________ with a mean of ____________________.

Test the hypotheses H0: There is no first-order autocorrelation vs. H1: There is positive first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.12, n = 45, k = 5, and α\alphaα = 0.05.

If the residuals in a regression analysis of time ordered data are not correlated, the value of the Durbin-Watson d statistic should be near ____________________.

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400. Then, the value of MSE is 560.

The total variation in y is equal to SSR + ____________________.

Suppose a multiple regression analysis involving 25 data points has sz2=1.8s _ { z } ^ { 2 } = 1.8sz2​=1.8 and SSE = 36. Then, the number of the independent variables must be:

The validity of a multiple regression model is tested using a(n) _________ test.

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

If the value of the Durbin-Watson test statistic, d, satisfies the inequalities d < dL or d > 4 - dL, where dL and dU are the critical values of d, we conclude that positive first-order autocorrelation exists.

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

In a multiple regression model, the following statistics are given: SSE = 100, R2 = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is:

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

For the following multiple regression model: $\hat { y } = 2 - 3 x _ { 1 } + 4 x _ { 2 } + 5 x _ { 3 }$ , a unit increase in x₁, holding x₂ and x₃ constant, results in:

Some of the requirements for the error variable in a multiple regression model are that the probability distribution is with a mean of .

Test the hypotheses H₀: There is no first-order autocorrelation vs. H₁: There is positive first-order autocorrelation, given that: Durbin-Watson Statistic d = 1.12, n = 45, k = 5, and $\alpha$ = 0.05.

Suppose a multiple regression analysis involving 25 data points has $s _ { z } ^ { 2 } = 1.8$ and SSE = 36. Then, the number of the independent variables must be:

If the value of the Durbin-Watson test statistic, d, satisfies the inequalities d < d_L or d > 4 - d_L, where d_L and d_U are the critical values of d, we conclude that positive first-order autocorrelation exists.

In a multiple regression model, the following statistics are given: SSE = 100, R² = 0.995, k = 5, and n = 15. Then, the coefficient of determination adjusted for degrees of freedom is: