NARRBEGIN: Real Estate Builder 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 $\begin{array}{l|ccccc} & d f & \text { SS } & M S & F & \text { Signif F } \\ \hline \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & \\ \text { Total } & 49 & 4820.0000 & & \end{array}$ \[\begin{array} { | l | c c c c | } \hline & \text { Coeff } & \text { st.error } & \boldsymbol { t }\boldsymbol { state } & \boldsymbol { P } \text {-value } \\ \hline \text { Intercept } & - 1.6335 & 5.807 \mathrm { 8 } & - 0.281 & 0 .798 \\ \text { Family Income } & 0.4485 & 0.1137 & 3.9545 & 0 .0003 \\ \text { Family Size } & 4.2615 & 0.8062 & 5.286 & 0 .0001 \\ \text { Education } & - 0.6517 & 0.4319 & - 1.509 & 0 .1383 \\ \hline \end{array}\] NARREND -{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?

The answer of NARRBEGIN: Real Estate Builder Real Estate Builder A real...

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

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.

Exam 17: Multiple Regression

NARRBEGIN: Real Estate Builder 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 df SS MS F Signif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff st.error -value Intercept -1.6335 5.807 -0.281 0.798 Family Income 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 NARREND -{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?

(Short Answer)

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Question 101

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

(Short Answer)

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Question 102

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

(Short Answer)

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Question 103

NARRBEGIN: Real Estate Builder 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 df SS MS F Signif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff st.error -value Intercept -1.6335 5.807 -0.281 0.798 Family Income 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 NARREND -{Real Estate Builder Narrative} Which of the independent variables in the model are significant at the 2% level?

(Short Answer)

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Question 104

Because of multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

(True/False)

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Question 105

The Durbin-Watson statistic, d, is defined as $d = \sum _ { i = 2 } ^ { n } \left( e _ { i } - e _ { i - 1 } \right) ^ { 2 } / \sum _ { i = 1 } ^ { n } e _ { i }$ , where e_i is the residual at time period i.

(True/False)

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Question 106

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

(Multiple Choice)

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Question 107

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

(True/False)

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Question 108

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.

(Short Answer)

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Question 109

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?

(Multiple Choice)

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Question 110

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

(Multiple Choice)

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Question 111

A multiple regression model has the form $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

(True/False)

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Question 112

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

(True/False)

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Question 113

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.

(True/False)

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Question 114

NARRBEGIN: Student's Final Grade 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 $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ , 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 $\hat { y } = 41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }$ PredictOr Coef SuDsv 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 Regression 3 3716 1238.667 6.558 Error 46 8688 188.870 Total 49 12404 NARREND -{Student's Final Grade Narrative} What is the adjusted coefficient of determination? What does this statistic tell you?

(Essay)

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Question 115

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

(Multiple Choice)

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Question 116

For a multiple regression model, the total variation in y can be expressed as:

(Multiple Choice)

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Question 117

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

(True/False)

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Question 118

If the Durbin-Watson statistic d has values smaller than 2, this indicates

(Multiple Choice)

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Question 119

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.

(True/False)

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Question 120

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

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

Because of multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

The Durbin-Watson statistic, d, is defined as $d = \sum _ { i = 2 } ^ { n } \left( e _ { i } - e _ { i - 1 } \right) ^ { 2 } / \sum _ { i = 1 } ^ { n } e _ { i }$ , where e_i is the residual at time period i.

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

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

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.

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

A multiple regression model has the form $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

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

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.

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

For a multiple regression model, the total variation in y can be expressed as:

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

If the Durbin-Watson statistic d has values smaller than 2, this indicates

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.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

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 Optional

Simple Linear Regression and Correlation

Filters

Exam 17: Multiple Regression

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

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

Because of multicollinearity, the t-tests of the individual coefficients may indicate that some independent variables are not linearly related to the dependent variable, when in fact they are.

The Durbin-Watson statistic, d, is defined as d=∑i=2n(ei−ei−1)2/∑i=1neid = \sum _ { i = 2 } ^ { n } \left( e _ { i } - e _ { i - 1 } \right) ^ { 2 } / \sum _ { i = 1 } ^ { n } e _ { i }d=∑i=2n​(ei​−ei−1​)2/∑i=1n​ei​ , where ei is the residual at time period i.

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

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

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.

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

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

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

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.

For the multiple regression model: y^=75+25x1−15x2+10x3\hat { 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:

For a multiple regression model, the total variation in y can be expressed as:

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

If the Durbin-Watson statistic d has values smaller than 2, this indicates

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.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

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 Optional

Simple Linear Regression and Correlation

Filters

The Durbin-Watson statistic, d, is defined as $d = \sum _ { i = 2 } ^ { n } \left( e _ { i } - e _ { i - 1 } \right) ^ { 2 } / \sum _ { i = 1 } ^ { n } e _ { i }$ , where e_i is the residual at time period i.

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

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.

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

A multiple regression model has the form $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ . The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

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