## Statistics for Management

Statistics

## Quiz 17 :

Multiple Regression

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Q16 Q16 Q16

In multiple regression analysis, when the response surface (the graphical depiction of the regression equation) hits every single point, the sum of squares for error SSE = 0, the standard error of estimate s

_{}= 0, and the coefficient of determination R^{2}= 1.Free

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Q70 Q70 Q70

The computer output for the multiple regression model is shown below.However, because of a printer malfunction some of the results are not shown.These are indicated by the boldface letters a to i.Fill in the missing results (up to three decimal places).
ANALYSIS OF VARIANCE

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Q71 Q71 Q71

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} Is there enough evidence at the 5% significance level to infer that the model is useful in predicting length of life?Free

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Q72 Q72 Q72

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{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?Free

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Q73 Q73 Q73

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{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?Free

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Q74 Q74 Q74

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{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?Free

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Q75 Q75 Q75

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} What is the coefficient of determination? What does this statistic tell you?Free

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Q76 Q76 Q76

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} What is the adjusted coefficient of determination in this situation? What does this statistic tell you?Free

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Q77 Q77 Q77

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} Interpret the coefficient b_{1}.Free

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Q78 Q78 Q78

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} Interpret the coefficient b_{2}.Free

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Q79 Q79 Q79

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 (x

_{1}), the cholesterol level (x_{2}), and the number of points that the individual's blood pressure exceeded the recommended value (x_{3}).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 + 1.79x_{1} 0.021x_{2} 0.061x_{3}ANALYSIS OF VARIANCE -{Life Expectancy Narrative} Interpret the coefficient b_{3}.Free

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Q80 Q80 Q80

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} What is the coefficient of determination? What does this statistic tell you?Free

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Q81 Q81 Q81

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} What is the adjusted coefficient of determination? What does this statistic tell you?Free

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Q82 Q82 Q82

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Does this data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final grade?Free

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Q83 Q83 Q83

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Does this data provide enough evidence to conclude at the 5% significance level that the final grade and the number of skipped lectures are linearly related?Free

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Q84 Q84 Q84

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{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?Free

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Q85 Q85 Q85

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Does this data provide enough evidence at the 1% significance level to conclude that the final grade and the midterm exam score are positively linearly related?Free

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Q86 Q86 Q86

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Interpret the coefficient b_{1}.Free

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Q87 Q87 Q87

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Interpret the coefficient b_{2}.Free

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Q88 Q88 Q88

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 , where y is the final grade (out of 100 points), x

_{1}is the number of lectures skipped, x_{2}is the number of late assignments, and x_{3}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 ANALYSIS OF VARIANCE -{Student's Final Grade Narrative} Interpret the coefficient b_{3}.Free

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Q89 Q89 Q89

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
ANOVA
-{Real Estate Builder Narrative} What percentage of the variability in house size is explained by this model?

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Q90 Q90 Q90

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
ANOVA
-{Real Estate Builder Narrative} Interpret the value of the Adjusted R-Square.

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Q91 Q91 Q91

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
ANOVA
-{Real Estate Builder Narrative} Which of the independent variables in the model are significant at the 2% level?

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Q92 Q92 Q92

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
ANOVA
-{Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually: = .01, .05, .10, or .15?

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Q93 Q93 Q93

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
ANOVA
-{Real Estate Builder Narrative} When the builder used a simple linear regression model with house size as the dependent variable and education as the independent variable, he obtained an R-square value of 23.0%.What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

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Q94 Q94 Q94

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
ANOVA
-{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: = .01, .05, .10, and .15?

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Q95 Q95 Q95

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
ANOVA
-{Real Estate Builder Narrative} Which of the following values for the level of significance is the smallest for which the regression model as a whole is significant: = .00005, .001, .01, and .05?

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Q96 Q96 Q96

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
ANOVA
-{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?

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Q97 Q97 Q97

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
ANOVA
-{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?

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Q98 Q98 Q98

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
ANOVA
-{Real Estate Builder Narrative} What minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home?

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Q99 Q99 Q99

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
ANOVA
-{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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Q100 Q100 Q100

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
ANOVA
-{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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Q101 Q101 Q101

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
ANOVA
-{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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Q102 Q102 Q102

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
ANOVA
-{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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Q103 Q103 Q103

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
ANOVA
-{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on education is significantly different from 0.What is the value of the relevant t-statistic?

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Q104 Q104 Q104

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
ANOVA
-{Real Estate Builder Narrative} What is the value of the calculated F-test statistic that is missing from the output for testing whether the whole regression model is significant?

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Q105 Q105 Q105

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
ANOVA
-{Real Estate Builder Narrative} At the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of education in the regression model?

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Q106 Q106 Q106

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
ANOVA
-{Real Estate Builder Narrative} What are the regression degrees of freedom that are missing from the output?

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Q107 Q107 Q107

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
ANOVA
-{Real Estate Builder Narrative} What are the residual degrees of freedom that are missing from the output?

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Q108 Q108 Q108

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
ANOVA
-{Real Estate Builder Narrative} What are the numerator and denominator degrees of freedom for the F-statistic?

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