A sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the average number of social activities per week (X6). Suppose the multiple regression equation is: Y' = 16.24 + 0.017X1 + 0.00028X2 +42X3 + 0.0012X4 + 0.09X5 + 26.8X6. Explain the meaning of b6.

A) For each additional social activity per week, their satisfaction index is expected to increase by 26.8 points. B) For each additional social activity per week, their satisfaction index is expected to increase by 2.68 points. C) For each additional10 points on the health status index, their satisfaction index is expected to increase by 0.9 points. D) For each additional$10,000 in assets, their satisfaction index is expected to increase by 12 points. E) For each additional living child, their satisfaction index is expected to increase by 42 points. A) For each additional social activity per week, their satisfaction index is expected to increase by 26.8 points. B) For each additional social activity per week, their satisfaction index is expected to increase by 2.68 points. C) For each additional10 points on the health status index, their satisfaction index is expected to increase by 0.9 points. D) For each additional$10,000 in assets, their satisfaction index is expected to increase by 12 points. E) For each additional living child, their satisfaction index is expected to increase by 42 points.

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X2). The multiple regression equation for this model is: Y = 125 - 3X + X2 where: Y = selling price (times $1,000) X = square feet of floor space (times 100) What is the difference in selling prices of a house with 1,650 square feet and one with 1,750 square feet?

A) $30 000 B) $3000 C) $31 000 D) $32 000 A) $30 000 B) $3000 C) $31 000 D) $32 000

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X2). The multiple regression equation for this model is: Y = 125 - 3X + X2 where: Y = selling price (times $1,000) X = square feet of floor space (times 100) What is the difference in selling prices of a house with 1,700 square feet and one with 1,800 square feet?

A) $30 000 B) $3000 C) $363 000 D) $32 000 A) $30 000 B) $3000 C) $363 000 D) $32 000

It has been hypothesized that overall academic success for freshmen at college as measured by grade point average (GPA) is a function of IQ scores (X1), hours spent studying each week (X2), and one's high school average (X3). Suppose the regression equation is: Y' = -6.9 + 0.055X1 + 0.107X2 + 0.0083X3. The multiple standard error is 6.313 and R2= 0.826. For which independent variable does a unit change have the greatest effect on the GPA?

A) IQ scores (X1) B) hours spent studying each week (X2) C) high school average (X3) A) IQ scores (X1) B) hours spent studying each week (X2) C) high school average (X3)

The following summary is from home heating costs, using mean outside temperature as X1 the number of centimeters of insulation as X2, and the presence of a garage as X3. Is the presence of the independent variable garage significant in predicting heating costs, when tested at the 0.01 level of significance?

A) Since the p-value is less than the level of significance, the null hypothesis is rejected, and so the garage should be included in the analysis. B) Since the p-value is less than the level of significance, the null hypothesis is accepted, and so the garage should not be included in the analysis. C) Since the p-value is more than the level of significance, the null hypothesis is accepted, and so the garage should not be included in the analysis. D) Since the p-value is more than the level of significance, the null hypothesis is rejected, and so the garage should be included in the analysis. A) Since the p-value is less than the level of significance, the null hypothesis is rejected, and so the garage should be included in the analysis. B) Since the p-value is less than the level of significance, the null hypothesis is accepted, and so the garage should not be included in the analysis. C) Since the p-value is more than the level of significance, the null hypothesis is accepted, and so the garage should not be included in the analysis. D) Since the p-value is more than the level of significance, the null hypothesis is rejected, and so the garage should be included in the analysis.

Exam 13: Multiple Regression and Correlation Analysis

i. A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation. ii. Autocorrelation often happens when data has been collected over periods of time. iii. Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different values of Y'.

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Question 1

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A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results: In the regression model, which of the following are dummy variables?

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i. If the null hypothesis $\beta$ ₄= 0 is not rejected, then the independent variable X₄ has a strong effect in predicting the dependent variable. ii. A dummy variable is added to the regression equation to control for error. iii. A variable whose possible outcomes are coded as a "1" or a "0" is called a strong independent variable.

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Question 3

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i. The multiple coefficient of determination, R², reports the proportion of the variation in Y that is explained by the variation in the set of independent variables. ii. The coefficient of multiple determination reports the strength of the association between the dependent variable and the set of independent variables. iii. A coefficient of multiple determination equaling -0.76 is definitely possible.

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Question 4

A sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied: age at the time of first marriage (X₁), annual income (X₂), number of children living (X₃), value of all assets (X₄), status of health in the form of an index (X₅), and the average number of social activities per week (X₆). Suppose the multiple regression equation is: Y' = 16.24 + 0.017X₁+ 0.00028X₂+42X₃+ 0.0012X₄+ 0.09X₅+ 26.8X₆. Explain the meaning of b₆.

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Question 5

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting average, home runs, stolen bases, errors, and team ERA. The number of degrees of freedom to be used in determining the critical value of t to be used in a hypothesis test of the regression coefficients is:

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Question 6

i. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. ii. A multiple coefficient of determination equaling -0.76 is definitely possible. iii. Multiple R²measures the proportion of explained variation relative to total variation.

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Question 7

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X²). The multiple regression equation for this model is: Y = 125 - 3X + X²where: Y = selling price (times $1,000) X = square feet of floor space (times 100) What is the difference in selling prices of a house with 1,650 square feet and one with 1,750 square feet?

(Multiple Choice)

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Question 8

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the strongest association with the dependent variable?

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Question 9

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data. What is the proportion of variation in tires produced by our predictor variables in the model?

(Multiple Choice)

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Question 10

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X²). The multiple regression equation for this model is: Y = 125 - 3X + X²where: Y = selling price (times $1,000) X = square feet of floor space (times 100) What is the difference in selling prices of a house with 1,700 square feet and one with 1,800 square feet?

(Multiple Choice)

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Question 11

It has been hypothesized that overall academic success for freshmen at college as measured by grade point average (GPA) is a function of IQ scores (X₁), hours spent studying each week (X₂), and one's high school average (X₃). Suppose the regression equation is: Y' = -6.9 + 0.055X₁+ 0.107X₂+ 0.0083X₃. The multiple standard error is 6.313 and R²= 0.826. For which independent variable does a unit change have the greatest effect on the GPA?

(Multiple Choice)

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Question 12

It is thought that there are a variety of factors that affect a teacher's salary. Using the following printout and sample data, determine whether the holding of a PhD degree is a significant variable when tested at the 10% level of significance.

(Multiple Choice)

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Question 13

The following summary is from home heating costs, using mean outside temperature as X₁the number of centimeters of insulation as X₂, and the presence of a garage as X₃. Is the presence of the independent variable garage significant in predicting heating costs, when tested at the 0.01 level of significance?

(Multiple Choice)

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Question 14

What is the measurement of explained variation?

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Question 15

Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output: Determine the multiple regression equation. _______________________

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Question 16

Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output: What is the effect on salary of an increase in age of two years if other variables are held constant?

(Multiple Choice)

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Question 17

i. The multiple standard error of estimate measures the variation about the regression plane when two independent variables are considered. ii. The multiple coefficient of determination, R², reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables. iii. The coefficient of multiple determination reports the strength of the association between the dependent variable and the set of independent variables.

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Question 18

Multiple regression analysis is applied when analyzing the relationship between

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Question 19

i. Multiple regression is used when two or more independent variables are used to predict a value of a single dependent variable. ii. The values of b₁, b_2, and b₃ in a multiple regression equation are called the net regression coefficients. They indicate the change in the predicted value for a unit change in one X when the other X variables are held constant. iii. Multiple regression analysis examines the relationship of several dependent variables on the independent variable.

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Question 20

Showing 1 - 20 of 128

i. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. ii. A multiple coefficient of determination equaling -0.76 is definitely possible. iii. Multiple R²measures the proportion of explained variation relative to total variation.

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the strongest association with the dependent variable?

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data. What is the proportion of variation in tires produced by our predictor variables in the model?

It is thought that there are a variety of factors that affect a teacher's salary. Using the following printout and sample data, determine whether the holding of a PhD degree is a significant variable when tested at the 10% level of significance.

What is the measurement of explained variation?

Multiple regression analysis is applied when analyzing the relationship between

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

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Exam 13: Multiple Regression and Correlation Analysis

i. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. ii. A multiple coefficient of determination equaling -0.76 is definitely possible. iii. Multiple R2 measures the proportion of explained variation relative to total variation.

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the strongest association with the dependent variable?

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data. What is the proportion of variation in tires produced by our predictor variables in the model?

It is thought that there are a variety of factors that affect a teacher's salary. Using the following printout and sample data, determine whether the holding of a PhD degree is a significant variable when tested at the 10% level of significance.

What is the measurement of explained variation?

Multiple regression analysis is applied when analyzing the relationship between

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

One-Sample Tests of Hypothesis

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

i. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. ii. A multiple coefficient of determination equaling -0.76 is definitely possible. iii. Multiple R²measures the proportion of explained variation relative to total variation.