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 sufficient evidence at the 5% significance level to infer that the number of points that the individual's blood pressure exceeded the recommended value and the age at death are negatively linearly related?

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

A multiple regression model has the form $\tilde { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ .As x3 increases by one unit,with x1 and x2 held constant,the y on average is expected to:

A) increase by 1 unit. B) increase by 12 units. C) decrease by 4 units. D) decrease by 16 units. A) increase by 1 unit. B) increase by 12 units. C) decrease by 4 units. D) decrease by 16 units.

Exam 17: Multiple Regression

In a multiple regression analysis involving 50 observations and 5 independent variables,the total variation in y is 475 and SSE = 71.25.Then,the coefficient of determination is 0.85.

(True/False)

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Question 101

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and $\alpha$ = 0.01.

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Question 102

A multiple regression equation includes 5 independent variables,and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

(Multiple Choice)

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Question 103

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

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Question 104

Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.

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Question 105

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to:

(Multiple Choice)

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Question 106

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.

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Question 107

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 sufficient evidence at the 5% significance level to infer that the number of points that the individual's blood pressure exceeded the recommended value and the age at death are negatively linearly related?

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Question 108

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

(Multiple Choice)

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Question 109

In reference to the equation $\tilde { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ ,the value 0.12 is the average change in y per unit change in x₁,when x₂ is held constant.

(True/False)

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Question 110

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination.Then,the adjusted coefficient of determination is:

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Question 111

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

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Question 112

A multiple regression model has the form $\tilde { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ .As x₃ increases by one unit,with x₁ and x₂ held constant,the y on average is expected to:

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Question 113

How do you go about checking for multicollinearity?

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Question 114

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

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Question 115

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400.Then,the value of MSE is 560.

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Question 116

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 average change in y per unit change in x₁.

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Question 117

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

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Question 118

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

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Question 119

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations,the numerator and denominator degrees of freedom for the critical value of F are,respectively,

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Question 120

Showing 101 - 120 of 156

Exam 17: Multiple Regression

In a multiple regression analysis involving 50 observations and 5 independent variables,the total variation in y is 475 and SSE = 71.25.Then,the coefficient of determination is 0.85.

Test the hypotheses H0: no first-order autocorrelation vs.H1: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and α\alphaα = 0.01.

A multiple regression equation includes 5 independent variables,and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

A practical way to identify multicollinearity is through the examination of a correlation ____________________ that shows the correlations of each variable with each of the other variables.

Multicollinearity is present when there is a high degree of correlation between the independent variables included in the regression model.

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to:

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.

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

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 0.12 is the average change in y per unit change in x1,when x2 is held constant.

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted coefficient of determination.Then,the adjusted coefficient of determination is:

One clue to the presence of multicollinearity is an independent variable known to be an important predictor that ends up having a regression coefficient that is not ____________________.

A multiple regression model has the form y~=8+3x1+5x2−4x3\tilde { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }y~​=8+3x1​+5x2​−4x3​ .As x3 increases by one unit,with x1 and x2 held constant,the y on average is expected to:

How do you go about checking for multicollinearity?

Discuss two indicators that can be found in an analysis that suggest multicollinearity is present.

A multiple regression model involves 40 observations and 4 independent variables produces a total variation in y of 100,000 and SSR = 80,400.Then,the value of MSE is 560.

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 average change in y per unit change in x1.

One of the consequences of multicollinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

In order to test the validity of a multiple regression model involving 5 independent variables and 30 observations,the numerator and denominator degrees of freedom for the critical value of F are,respectively,

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

Test the hypotheses H₀: no first-order autocorrelation vs.H₁: first-order autocorrelation,given that: Durbin-Watson Statistic d = 1.89,n = 28,k = 3,and $\alpha$ = 0.01.

In reference to the equation $\tilde { y } = - 0.80 + 0.12 x _ { 1 } + 0.08 x _ { 2 }$ ,the value 0.12 is the average change in y per unit change in x₁,when x₂ is held constant.

A multiple regression model has the form $\tilde { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 3 }$ .As x₃ increases by one unit,with x₁ and x₂ held constant,the y on average is expected to:

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 average change in y per unit change in x₁.