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

@#LAT-DLM& vs. @#LAT-DLM& Rejection region: | t | > t 0.

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} Does this data provide enough evidence at the 5% significance level to conclude that the final grade and the number of late assignments are negatively linearly related?

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

Exam 17: Multiple Regression

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

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Question 21

For a multiple regression model the following statistics are given: Total variation in y = 250,SSE = 50,k = 4,and n = 20.Then,the coefficient of determination adjusted for the degrees of freedom is:

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Question 22

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

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Question 23

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array} \end{array} ANOVA \begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \\ \text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array} -{Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually: \alpha = .01,.05,.10,and .15?$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually: $\alpha$ = .01,.05,.10,and .15?

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Question 24

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

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Question 25

In multiple regression analysis,the ratio MSR/MSE yields the:

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Question 26

In a multiple regression analysis involving 4 independent variables and 30 data points,the number of degrees of freedom associated with the sum of squares for error,SSE,is 25.

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Question 27

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 (x₁),the cholesterol level (x₂),and the number of points that the individual's blood pressure exceeded the recommended value (x₃).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 + 1.79x₁ -0.021x₂ -0.061x₃ Predicter Coef StDev T Constant 55.8 11.8 4.729 1.79 0.44 4.068 -0.021 0.011 -1.909 -0.016 0.014 -1.143 $S = 9.47 \quad R - S q = 22.5 \%$ ANALYSIS OF VARIANCE Source of Variation Repressian 3 936 312 3.477 Error 36 3230 89.722 Total 39 4166 -{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?

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Question 28

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array} \end{array} ANOVA \begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \\ \text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array} -{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on income is significantly different from 0.What is the value of the relevant t-statistic?$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{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?

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Question 29

The coefficient of determination ranges from:

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Question 30

In a multiple regression analysis,if the model provides a poor fit,this indicates that:

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Question 31

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array} \end{array} ANOVA \begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \\ \text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array} -{Real Estate Builder Narrative} At the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of income in the regression model?$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{Real Estate Builder Narrative} At the 0.01 level of significance,what conclusion should the builder draw regarding the inclusion of income in the regression model?

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Question 32

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),x₁ is the number of lectures skipped,x₂ is the number of late assignments,and x₃ 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 $\tilde { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$ Predicter Coef StDsv T Constant 41.6 17.8 2.337 -3.18 1.66 -1.916 -1.17 1.13 -1.035 0.63 0.13 4.846 $S = 13.74 \quad R - S q = 30.0 \%$ ANALYSIS OF VARIANCE Source of Variation Repressian 3 3716 1238.667 6.558 Esrar 46 8688 188.870 Total 49 12404 -{Student's Final Grade Narrative} Does this data provide enough evidence at the 5% significance level to conclude that the final grade and the number of late assignments are negatively linearly related?

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Question 33

In multiple regression,the standard error of estimate is defined by $s _ { z } = \sqrt { \operatorname { SSE } / ( n - k ) }$ ,where n is the sample size and k is the number of independent variables.

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Question 34

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $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} One individual in the sample had an annual income of $100,000,a family size of 10,and an education of 16 years.This individual owned a home with an area of 7,000 square feet.What is the residual (in hundreds of square feet)for this data point?$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{Real Estate Builder Narrative} One individual in the sample had an annual income of $100,000,a family size of 10,and an education of 16 years.This individual owned a home with an area of 7,000 square feet.What is the residual (in hundreds of square feet)for this data point?

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Question 35

When an additional explanatory variable is introduced into a multiple regression model,coefficient of determination adjusted for degrees of freedom can never decrease.

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Question 36

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array} \end{array} ANOVA \begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \\ \text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array} -{Real Estate Builder Narrative} What are the numerator and denominator degrees of freedom for the F-statistic?$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{Real Estate Builder Narrative} What are the numerator and denominator degrees of freedom for the F-statistic?

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Question 37

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

(Multiple Choice)

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Question 38

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 autocorrelation exists.

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Question 39

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 Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA $Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT \begin{array}{l} \text { Regression Statistics }\\ \begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adjusted R Square } & 0.726 \\ \text { Standard Error } & 5.195 \\ \text { Observations } & 50 \end{array} \end{array} ANOVA \begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { St. Error } & \boldsymbol { t }\boldsymbol {Sat } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .7798 \\ \text { Family Incame } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array} -{Real Estate Builder Narrative} Interpret the value of the Adjusted R-Square.$ Coeff St. Error -value Intercept -1.6335 5.807 -0.281 0.7798 Family Incame 0.4485 0.1137 3.9545 0.0003 Family Size 4.2615 0.8062 5.286 0.0001 Education -0.6517 0.4319 -1.509 0.1383 -{Real Estate Builder Narrative} Interpret the value of the Adjusted R-Square.

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Question 40

Showing 21 - 40 of 156

The coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

For a multiple regression model the following statistics are given: Total variation in y = 250,SSE = 50,k = 4,and n = 20.Then,the coefficient of determination adjusted for the degrees of freedom is:

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

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

In multiple regression analysis,the ratio MSR/MSE yields the:

In a multiple regression analysis involving 4 independent variables and 30 data points,the number of degrees of freedom associated with the sum of squares for error,SSE,is 25.

The coefficient of determination ranges from:

In a multiple regression analysis,if the model provides a poor fit,this indicates that:

In multiple regression,the standard error of estimate is defined by $s _ { z } = \sqrt { \operatorname { SSE } / ( n - k ) }$ ,where n is the sample size and k is the number of independent variables.

When an additional explanatory variable is introduced into a multiple regression model,coefficient of determination adjusted for degrees of freedom can never decrease.

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

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 autocorrelation exists.

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 coefficient of determination ____________________ for degrees of freedom takes into account the sample size and the number of independent variables when assessing model fit.

For a multiple regression model the following statistics are given: Total variation in y = 250,SSE = 50,k = 4,and n = 20.Then,the coefficient of determination adjusted for the degrees of freedom is:

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

In reference to the equation y~=−0.80+0.12x1+0.08x2\tilde { 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.

In multiple regression analysis,the ratio MSR/MSE yields the:

In a multiple regression analysis involving 4 independent variables and 30 data points,the number of degrees of freedom associated with the sum of squares for error,SSE,is 25.

The coefficient of determination ranges from:

In a multiple regression analysis,if the model provides a poor fit,this indicates that:

In multiple regression,the standard error of estimate is defined by sz=SSE⁡/(n−k)s _ { z } = \sqrt { \operatorname { SSE } / ( n - k ) }sz​=SSE/(n−k)​ ,where n is the sample size and k is the number of independent variables.

When an additional explanatory variable is introduced into a multiple regression model,coefficient of determination adjusted for degrees of freedom can never decrease.

If the Durbin-Watson statistic has a value close to 0,which assumption is violated?

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 autocorrelation exists.

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

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

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

In multiple regression,the standard error of estimate is defined by $s _ { z } = \sqrt { \operatorname { SSE } / ( n - k ) }$ ,where n is the sample size and k is the number of independent 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 autocorrelation exists.