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:

A) 0.992 B) 0.900 C) 0.955 D) 0.855 A) 0.992 B) 0.900 C) 0.955 D) 0.855

Exam 17: Multiple Regression

A high value of the coefficient of determination significantly above 0 in multiple regression,accompanied by insignificant t-statistics on all parameter estimates,very often indicates a high correlation between independent variables in the model.

(True/False)

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Question 41

In calculating the standard error of the estimate, $s _ { z } = \sqrt { \mathrm { MSE } }$ ,there are (n $\le$ k $\le$ 1)degrees of freedom,where n is the sample size and k is the number of independent variables in the model.

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Question 42

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:

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Question 43

One of the consequences of multicollinearity in multiple regression is biased estimates on the slope coefficients.

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Question 44

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

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Question 45

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

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Question 46

A(n)____________________ value of the F-test statistic indicates that the multiple regression model is valid.

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Question 47

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

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Question 48

If multicollinearity exists among the independent variables included in a multiple regression model,then:

(Multiple Choice)

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Question 49

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

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Question 50

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

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Question 51

The Durbin-Watson d statistic is used to check the assumption of normality.

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Question 52

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

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Question 53

In a multiple regression analysis involving 6 independent variables,the total variation in y is 900 and SSR = 600.What is the value of SSE?

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Question 54

In a multiple regression analysis,there are 20 data points and 4 independent variables,and the sum of the squared differences between observed and predicted values of y is 180.The standard error of estimate will be:

(Multiple Choice)

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Question 55

Which of the following statements regarding multicollinearity is not true?

(Multiple Choice)

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Question 56

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

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Question 57

A multiple regression model has the form $\tilde { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ .The coefficient b₁ is interpreted as the change in the average value of y per unit change in holding constant.

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Question 58

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 $10,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square fee (House = 10.00).What is the residual (in hundreds of square feet)for this data point?$ 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 $10,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square fee (House = 10.00).What is the residual (in hundreds of square feet)for this data point?

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Question 59

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

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Question 60

Showing 41 - 60 of 156

Exam 17: Multiple Regression

A high value of the coefficient of determination significantly above 0 in multiple regression,accompanied by insignificant t-statistics on all parameter estimates,very often indicates a high correlation between independent variables in the model.

In calculating the standard error of the estimate, sz=MSEs _ { z } = \sqrt { \mathrm { MSE } }sz​=MSE​ ,there are (n ≤\le≤ k ≤\le≤ 1)degrees of freedom,where n is the sample size and k is the number of independent variables in the model.

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:

One of the consequences of multicollinearity in multiple regression is biased estimates on the slope coefficients.

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

Multicollinearity affects the t-tests of the individual coefficients as well as the F-test in the analysis of variance for regression because the F-test combines the t-tests into a single test.

A(n)____________________ value of the F-test statistic indicates that the multiple regression model is valid.

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

If multicollinearity exists among the independent variables included in a multiple regression model,then:

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

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

The Durbin-Watson d statistic is used to check the assumption of normality.

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

In a multiple regression analysis involving 6 independent variables,the total variation in y is 900 and SSR = 600.What is the value of SSE?

In a multiple regression analysis,there are 20 data points and 4 independent variables,and the sum of the squared differences between observed and predicted values of y is 180.The standard error of estimate will be:

Which of the following statements regarding multicollinearity is not true?

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

A multiple regression model has the form y~=b0+b1x1+b2x2\tilde { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }y~​=b0​+b1​x1​+b2​x2​ .The coefficient b1 is interpreted as the change in the average value of y per unit change in ________ holding ________ constant.

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 calculating the standard error of the estimate, $s _ { z } = \sqrt { \mathrm { MSE } }$ ,there are (n $\le$ k $\le$ 1)degrees of freedom,where n is the sample size and k is the number of independent variables in the model.

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:

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

A multiple regression model has the form $\tilde { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ .The coefficient b₁ is interpreted as the change in the average value of y per unit change in holding constant.