Question 1

The range of the values of the Durbin-Watson statistic,d,is 0 $\le$ d $\le$ 4.

Accepted Answer

A) True 
 B)False

Question 2

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 b3.

Accepted Answer

b₃ = 0.016.This tells us for

Question 3

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 minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home?

Accepted Answer

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

Question 4

____________________ 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 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} What is the adjusted coefficient of determination in this situation? What does this statistic tell you?

Accepted Answer

R² adjusted is 0.16

Question 6

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 - dL,we conclude that positive first-order autocorrelation exists.

Accepted Answer

A) True 
 B)False

Question 7

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with $\alpha$ = .05,n = 20,and there are two independent variables in the model,the critical values for the test are dL = __________ and dU = __________,respectively.

Accepted Answer

The answer of Given that the Durbin-Watson test is conducted...

Question 8

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

Accepted Answer

Question 9

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ .

Accepted Answer

A) True 
 B)False

Question 10

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 11

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 12

Senior Medical Students
A professor of Anatomy wanted to develop a multiple regression model to predict the students' grades in her fourth-year medical course.She decides that the two most important factors are the student's grade point average in the first three years and the student's major.She proposes the model y = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0 + $\beta$S1U1B13S1U1B0xS1U1B13S1U1B0 + $\varepsilon$,where y = Fourth-year medical course final score (out of 100),xS1U1B11S1U1B0 = G.P.A.in first three years (range from 0 to 12),xS1U1B12S1U1B0 = 1 if student's major is medicine and 0 if not,and xS1U1B13S1U1B0 = 1 if student's major is biology and 0 if not.The computer output is shown below.
THE REGRESSION EQUATION IS
y = 9.14 + 6.73xS1U1B11S1U1B0 + 10.42xS1U1B12S1U1B0 + 5.16xS1U1B13S1U1B0
 $$\begin{array} { | c | c c c | } 
\hline \text { Predictor } & \text { Coef } & \text { StDev } & T \
\hline \text { Constant } & 9.14 & 7.10 & 1.287 \
\boldsymbol { x } _ { 1 } & 6.73 & 1.91 & 3.524 \
\boldsymbol { x } _ { 2 } & 10.42 & 4.16 & 2.505 \
\boldsymbol {x } _ { 3 } & 5.16 & 3.93 & 1.313 \
\hline
\end{array}$$ $$S = 15.0 \quad R - S q = 44.2 \%$$ ANALYSIS OF VARIANCE
 $\begin{array}{l|ccccc}
\text { Source of Variation } & d f & \text { SS } & M S & F \
\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \
\text { Error } & 96 & 21553 & 224.510 & \
\hline \text { Total } & 99 & 38651 & &
\end{array}$

-In multiple regression analysis,the adjusted coefficient of determination is adjusted for the number of independent variables and the sample size.

Accepted Answer

A) True 
 B)False

Question 13

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} Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life?

Accepted Answer

@#LAT-DLM& @#LAT-DLM& At least one @#LAT-DLM&_i is not equal

Question 14

Small values of the Durbin-Watson statistic d (d < 2)indicate a negative first-order autocorrelation.

Accepted Answer

A) True 
 B)False

Question 15

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} What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

R² = 0.225.This means that 22

Question 16

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} Is there enough evidence at the 5% significance level to infer that the cholesterol level and the age at death are negatively linearly related?

Accepted Answer

@#LAT-DLM& vs. @#LAT-DLM& Rejection region: t < -t<sub>0.05,

Question 17

If the value of the Durbin-Watson statistic,d,satisfies the inequality dL $\le$ d $\le$ dU,where dL and dU are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

Accepted Answer

A) True 
 B)False

Question 18

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;zer

Question 19

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 20

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

Accepted Answer

A)  k,where k is the number of independent variables included in the model. 
B)  1.0 
C)  0.0 
D)  None of these choices. 
A)  k,where k is the number of independent variables included in the model. 
B)  1.0 
C)  0.0 
D)  None of these choices.

The range of the values of the Durbin-Watson statistic,d,is 0 $\le$ d $\le$ 4.

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

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 - d_L,we conclude that positive first-order autocorrelation exists.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with $\alpha$ = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

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

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ .

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 ____________________.

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

Small values of the Durbin-Watson statistic d (d < 2)indicate a negative first-order autocorrelation.

If the value of the Durbin-Watson statistic,d,satisfies the inequality d_L $\le$ d $\le$ d_U,where d_L and d_U are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

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

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:

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

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

Exam 17: Multiple Regression

The range of the values of the Durbin-Watson statistic,d,is 0 ≤\le≤ d ≤\le≤ 4.

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

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 - dL,we conclude that positive first-order autocorrelation exists.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with α\alphaα = .05,n = 20,and there are two independent variables in the model,the critical values for the test are dL = __________ and dU = __________,respectively.

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

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is H0:β1=β2=β3H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }H0​:β1​=β2​=β3​ .

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 ____________________.

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

Small values of the Durbin-Watson statistic d (d < 2)indicate a negative first-order autocorrelation.

If the value of the Durbin-Watson statistic,d,satisfies the inequality dL ≤\le≤ d ≤\le≤ dU,where dL and dU are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

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

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:

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

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

The range of the values of the Durbin-Watson statistic,d,is 0 $\le$ d $\le$ 4.

If the value of the Durbin-Watson test statistic,d,satisfies the inequality d > 4 - d_L,we conclude that positive first-order autocorrelation exists.

Given that the Durbin-Watson test is conducted to test for positive first-order autocorrelation with $\alpha$ = .05,n = 20,and there are two independent variables in the model,the critical values for the test are d_L = __________ and d_U = __________,respectively.

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

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$ .

If the value of the Durbin-Watson statistic,d,satisfies the inequality d_L $\le$ d $\le$ d_U,where d_L and d_U are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

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

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:

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