Question 1

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

Accepted Answer

A) True 
 B)False

Question 2

For the multiple regression model: $\tilde { y } = 75 + 25 x _ { 1 } - 15 x _ { 2 } + 10 x _ { 3 }$ ,if x2 were to increase by 5,holding x1 and x3 constant,the value of y will:

Accepted Answer

A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75. 
A)  increase by 5. 
B)  increase by 75. 
C)  decrease on average by 5. 
D)  decrease on average by 75.

Question 3

The range of the values of the Durbin-Watson statistic d is ____________________.

Accepted Answer

The answer of The range of the values of the...

Question 4

Multiple regression has four requirements for the error variable.One is that the probability distribution of the error variable is ____________________.

Accepted Answer

The answer of Multiple regression has four requirements for the...

Question 5

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 b2.

Accepted Answer

b₂ = -0.021.This tells us tha

Question 6

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 =

Question 7

In order to test the significance of a multiple regression model involving 4 independent variables and 25 observations,the numerator and denominator degrees of freedom for the critical value of F are 3 and 21,respectively.

Accepted Answer

A) True 
 B)False

Question 8

If the value of the Durbin-Watson statistic d is small (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 9

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 10

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} 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 11

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 b2.

Accepted Answer

b₂ =-1.17.This tells us that

Question 12

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

Accepted Answer

A)  k - 1 
B)  n - k 
C)  n - 1 
D)  n - k - 1 
A)  k - 1 
B)  n - k 
C)  n - 1 
D)  n - k - 1

Question 13

In multiple regression analysis,when the response surface (the graphical depiction of the regression equation)hits every single point,the sum of squares for error SSE = 0,the standard error of estimate s $\varepsilon$  = 0,and the coefficient of determination R2 = 1.

Accepted Answer

A) True 
 B)False

Question 14

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

Accepted Answer

The answer of An adverse effect of multicollinearity is that...

Question 15

There are several clues to the presence of multicollinearity.One clue is when a regression coefficient exhibits the wrong ____________________.

Accepted Answer

The answer of There are several clues to the presence...

Question 16

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 the regression model as a whole is significant: $\alpha$= .00005,.001,.01,and .05?

Accepted Answer

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

Question 17

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 18

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

Accepted Answer

A) True 
 B)False

Question 19

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s $\varepsilon$  are both small,the coefficient of determination R2 is close to 1,and the value of the test statistic F is large.

Accepted Answer

A) True 
 B)False

Question 20

There are several clues to the presence of multicollinearity.One clue is when an independent variable is added or deleted,the regression coefficients for the other variables ____________________.

Accepted Answer

The answer of There are several clues to the presence...

Exam 17: Multiple Regression

A small value of F indicates that most of the variation in y is explained by the regression equation and that the model is useful.

For the multiple regression model: y~=75+25x1−15x2+10x3\tilde { y } = 75 + 25 x _ { 1 } - 15 x _ { 2 } + 10 x _ { 3 }y~​=75+25x1​−15x2​+10x3​ ,if x2 were to increase by 5,holding x1 and x3 constant,the value of y will:

The range of the values of the Durbin-Watson statistic d is ____________________.

Multiple regression has four requirements for the error variable.One is that the probability distribution of the error variable is ____________________.

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 order to test the significance of a multiple regression model involving 4 independent variables and 25 observations,the numerator and denominator degrees of freedom for the critical value of F are 3 and 21,respectively.

If the value of the Durbin-Watson statistic d is small (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:

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

In multiple regression analysis,when the response surface (the graphical depiction of the regression equation)hits every single point,the sum of squares for error SSE = 0,the standard error of estimate s ε\varepsilonε = 0,and the coefficient of determination R2 = 1.

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

There are several clues to the presence of multicollinearity.One clue is when a regression coefficient exhibits the wrong ____________________.

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

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

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s ε\varepsilonε are both small,the coefficient of determination R2 is close to 1,and the value of the test statistic F is large.

There are several clues to the presence of multicollinearity.One clue is when an independent variable is added or deleted,the regression coefficients for the other variables ____________________.

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

For the multiple regression model: $\tilde { y } = 75 + 25 x _ { 1 } - 15 x _ { 2 } + 10 x _ { 3 }$ ,if x₂ were to increase by 5,holding x₁ and x₃ constant,the value of y will:

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 multiple regression analysis,when the response surface (the graphical depiction of the regression equation)hits every single point,the sum of squares for error SSE = 0,the standard error of estimate s _{$\varepsilon$} = 0,and the coefficient of determination R² = 1.

A multiple regression model is assessed to be good if the error sum of squares SSE and the standard error of estimate s _{$\varepsilon$} are both small,the coefficient of determination R² is close to 1,and the value of the test statistic F is large.