Question 1

When an additional explanatory variable is introduced into a multiple regression model,the coefficient of determination will never decrease.

Accepted Answer

A) True 
 B)False  True

Question 2

A multiple regression equation has a coefficient of determination of 0.81.Then,the percentage of the variation in y that is explained by the regression equation is 90%.

Accepted Answer

A) True 
 B)False  False

Question 3

The problem of multicollinearity arises when the:

Accepted Answer

A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  None of these choices. 
A)  dependent variables are highly correlated with one another. 
B)  independent variables are highly correlated with one another. 
C)  independent variables are highly correlated with the dependent variable. 
D)  None of these choices. B

Question 4

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 =

Question 5

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H0: ____________________ (there is/there is no)first-order autocorrelation.

Accepted Answer

Question 6

Student's Final Grade
A statistics professor investigated some of the factors that affect an individual student's final grade in her course.She proposed the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + €$ ,where y is the final grade (out of 100 points),xS1U1B11S1U1B0 is the number of lectures skipped,xS1U1B12S1U1B0 is the number of late assignments,and xS1U1B13S1U1B0 is the midterm exam score (out of 100).The professor recorded the data for 50 randomly selected students.The computer output is shown below.
THE REGRESSION EQUATION IS $$\tilde { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$$ $$\begin{array} { | c | c c c | } 
\hline \text { Predicter } & \text { Coef } & \text { StDsv } & T \
\hline \text { Constant } & 41.6 & 17.8 & 2.337 \
\boldsymbol { x } _ { 1 } & - 3.18 & 1.66 & - 1.916 \
x _ { 2 } & - 1.17 & 1.13 & - 1.035 \
x _ { 3 } & 0.63 & 0.13 & 4.846 \
\hline
\end{array}$$ $$S = 13.74 \quad R - S q = 30.0 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { SS} & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repressian } & 3 & 3716 & 1238.667 & 6.558 \
\text { Esrar } & 46 & 8688 & 188.870 & \
\hline \text { Total } & 49 & 12404 & & \
\hline
\end{array}$$
-{Student's Final Grade Narrative} Interpret the coefficient b3.

Accepted Answer

b₃ = 0.63.This tells us that for each add

Question 7

For the following multiple regression model: $\tilde { y } = 2 - 3 x _ { 1 } + 4 x _ { 2 } + 5 x _ { 3 }$ ,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 8

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Accepted Answer

A) True 
 B)False

Question 9

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 10

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

Accepted Answer

A) True 
 B)False

Question 11

A multiple regression model involves 10 independent variables and 30 observations.If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs.$\neq$ 0)the critical value will be:

Accepted Answer

A)  2.228 
B)  2.093 
C)  1.729 
D)  1.697 
A)  2.228 
B)  2.093 
C)  1.729 
D)  1.697

Question 12

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
   $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \
\text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$
-{Real Estate Builder Narrative} What is the predicted house size for an individual earning an annual income of $40,000,having a family size of 4,and having 13 years of education?

Accepted Answer

The answer of Real Estate Builder
A real estate builder wishes...

Question 13

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
   $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \
\text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$
-{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on education is significantly different from 0.What is the value of the relevant t-statistic?

Accepted Answer

The answer of Real Estate Builder
A real estate builder wishes...

Question 14

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 15

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 16

In a multiple regression model,the value of the coefficient of determination has to fall between

Accepted Answer

A)  -1 and +1. 
B)  0 and +1. 
C)  -1 and 0. 
D)  None of these choices. 
A)  -1 and +1. 
B)  0 and +1. 
C)  -1 and 0. 
D)  None of these choices.

Question 17

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
 $$\begin{array} { | c | c c c | } 
\hline \text { Predicter } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 55.8 & 11.8 & 4.729 \
\boldsymbol { x } _ { 1 } & 1.79 & 0.44 & 4.068 \
x_ { 2 } & - 0.021 & 0.011 & - 1.909 \
x _ { 3 } & - 0.016 & 0.014 & - 1.143 \
\hline
\end{array}$$ $$S = 9.47 \quad R - S q = 22.5 \%$$ ANALYSIS OF VARIANCE
 $$\begin{array} { | l | c c c c | } 
\hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { SS } & \boldsymbol { M S } & \boldsymbol { F } \
\hline \text { Repressian } & 3 & 936 & 312 & 3.477 \
\text { Error } & 36 & 3230 & 89.722 & \
\hline \text { Total } & 39 & 4166 & & \
\hline
\end{array}$$
-{Life Expectancy Narrative} Interpret the coefficient b1.

Accepted Answer

b₁ = 1.79.This tells us for e

Question 18

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s $\varepsilon$  are both large,the coefficient of determination R2 is close to 0,and the value of the test statistic F is large.

Accepted Answer

A) True 
 B)False

Question 19

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
   $$\begin{array} { | l | c c c c | } 
\hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \
\hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \
\text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \
\text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \
\text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \
\hline
\end{array}$$
-{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 Real Estate Builder
A real estate builder wishes...

Question 20

A multiple regression model has the form: $\tilde { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }$ .As x2 increases by one unit,holding x1 constant,then the value of y will increase by:

Accepted Answer

A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices 
A)  7.25 units 
B)  6 units on average 
C)  2 units 
D)  None of these choices

Exam 17: Multiple Regression

When an additional explanatory variable is introduced into a multiple regression model,the coefficient of determination will never decrease.

A multiple regression equation has a coefficient of determination of 0.81.Then,the percentage of the variation in y that is explained by the regression equation is 90%.

The problem of multicollinearity arises when the:

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.

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H0: ____________________ (there is/there is no)first-order autocorrelation.

For the following multiple regression model: y~=2−3x1+4x2+5x3\tilde { 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:

Multicollinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

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

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

A multiple regression model involves 10 independent variables and 30 observations.If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. ≠\neq= 0)the critical value will be:

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

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

In a multiple regression model,the value of the coefficient of determination has to fall between

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s ε\varepsilonε are both large,the coefficient of determination R2 is close to 0,and the value of the test statistic F is large.

A multiple regression model has the form: y~=5.25+2x1+6x2\tilde { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }y~​=5.25+2x1​+6x2​ .As x2 increases by one unit,holding x1 constant,then the value of y will increase by:

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: 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

A: Simple Linear Regression and Correlation

B: Simple Linear Regression and Correlation

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

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.

To use the Durbin-Watson test to test for positive first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

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

A multiple regression model involves 10 independent variables and 30 observations.If we want to test at the 5% significance level whether one of the coefficients is = 0 (vs. $\neq$ 0)the critical value will be:

A multiple regression model is assessed to be poor if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both large,the coefficient of determination R² is close to 0,and the value of the test statistic F is large.

A multiple regression model has the form: $\tilde { y } = 5.25 + 2 x _ { 1 } + 6 x _ { 2 }$ .As x₂ increases by one unit,holding x₁ constant,then the value of y will increase by: