A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders. In a regression analysis, the dependent variable Y is the increase in bus riders (in thousands of persons) from the start of the test until its conclusion. The independent variables are X1 = the number (in thousands) of free maps distributed and a binary variable X2 = 1 if the city has free downtown parking, 0 otherwise. The estimated regression equation is $\hat { Y } = 1.32 + 0.0345 X _ { 1 } - 1.45 X _ { 2 }$ . In city 3, the observed Y value is 7.3, X1 = 140, and X2 = 0. The residual for city 3 (in thousands) is:

A) 6.15. B) 1.15. C) 4.83. D) 1.57. A) 6.15. B) 1.15. C) 4.83. D) 1.57.

Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? \[\begin{array}{l} \begin{array} { | r | r | l | r | l | l | } \hline & \mathrm { R } ^ { 2 } & 0.499 & & & \\ \hline & \text { Adjusted } \mathrm { R } ^ { 2 } & 0.444 & \mathrm { n } & 91 & \\ \hline & \mathrm { R } & 0.707 & \mathrm { k } & 9 & \\ \hline & \text { Std. Error } & 4.019 & \text { Dep. Var. } & \text { HwyMPG } & \\ \hline \end{array}\\ \begin{array} { l r r r r r } \hline \text { Source } & \text { SS } & d f & M S & F & p \text {-value } \\ \hline \text { Regression } & 1,305.7251 & 9 & 145.0806 & 8.98 & .0000 \\ \text { Residual } & 1,308.3848 & 81 & 16.1529 & & \\ \hline \text { Total } & 2,614.1099 & 90 & & & \\ \hline \end{array} \end{array}\]

A) Statistically significant but large error in the MPG predictions B) Statistically significant and quite small MPG prediction errors C) Not quite significant, but predictions should be very good D) Not a significant regression at any customary level of ? A) Statistically significant but large error in the MPG predictions B) Statistically significant and quite small MPG prediction errors C) Not quite significant, but predictions should be very good D) Not a significant regression at any customary level of ?

If SSR = 3600, SSE = 1200, and SST = 4800, then R2 is:

A) .5000 B) .7500 C) .3333 D) .2500 A) .5000 B) .7500 C) .3333 D) .2500

Part of a regression output is provided below. Some of the information has been omitted. \[\begin{array} { l c c c c } \hline \text { Source of variation } & S S & d f & M S & F \\ \hline \text { Regression } & 3177.17 & 2 & 1588.6 & \\ \text { Residual } & & 17 & 17.717 & \\ \text { Total } & 3478.36 & 19 & & \\ \hline \end{array}\] The approximate value of F is:

A) 1605.7. B) 0.9134. C) 89.66. D) impossible to calculate with the given information. A) 1605.7. B) 0.9134. C) 89.66. D) impossible to calculate with the given information.

Exam 13: Multiple Regression

A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders. In a regression analysis, the dependent variable Y is the increase in bus riders (in thousands of persons) from the start of the test until its conclusion. The independent variables are X₁ = the number (in thousands) of free maps distributed and a binary variable X₂ = 1 if the city has free downtown parking, 0 otherwise. The estimated regression equation is $\hat { Y } = 1.32 + 0.0345 X _ { 1 } - 1.45 X _ { 2 }$ . In city 3, the observed Y value is 7.3, X₁ = 140, and X₂ = 0. The residual for city 3 (in thousands) is:

(Multiple Choice)

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Question 41

Refer to the following regression results. The dependent variable is Abort (the number of abortions per 1000 women of childbearing age). The regression was estimated using data for the 50 U.S. states with these predictors: EdSpend = public K-12 school expenditure per capita, Age = median age of population, Unmar = percent of total births by unmarried women, Infmor = infant mortality rate in deaths per 1000 live births. Variable Coefficients Standard Error t- Stat Intercept -19.244 25.387 -0.758 EdSpend 0.0080040 0.0054472 1.469 Age 0.76012 0.66914 1.136 Unmar 0.98629 0.22132 4.456 InfMor -3.7848 1.0173 -3.720 Which statement is not supported by a two-tailed test?

(Multiple Choice)

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Question 42

Which is a characteristic of the variance inflation factor (VIF)?

(Multiple Choice)

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Question 43

When autocorrelation is present, the estimates of the coefficients will be unbiased.

(True/False)

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Question 44

Which of the following would be most useful in checking the normality assumption of the errors in a regression model?

(Multiple Choice)

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Question 45

In a multiple regression with 3 predictors in a sample of 25 U.S. cities, we would use F_3,21 in a test of overall significance.

(True/False)

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Question 46

Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? 0.499 Adjusted 0.444 91 0.707 9 Std. Error 4.019 Dep. Var. HwyMPG Source SS df MS F p -value Regression 1,305.7251 9 145.0806 8.98 .0000 Residual 1,308.3848 81 16.1529 Total 2,614.1099 90

(Multiple Choice)

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Question 47

Which is not a name often given to an independent variable that takes on just two values (0 or 1) according to whether or not a given characteristic is absent or present?

(Multiple Choice)

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Question 48

Analyze the regression results below (n = 33 cars in 1993) using the concepts you have learned about multiple regression. Circle things of interest and write comments in the margin. Make a prediction for CityMPG for a car with EngSize = 2.5, ManTran = 1, Length = 184, Wheelbase = 104, Weight = 3000, and Domestic = 0 (show your work). The variables are CityMPG = city MPG (miles per gallon by EPA rating); EngSize = engine size (liters); ManTran = 1 if manual transmission available, 0 otherwise; Length = vehicle length (inches); Wheelbase = vehicle wheelbase (inches); Weight = vehicle weight (pounds); Domestic = 1 if U.S. manufacturer, 0 otherwise.

(Essay)

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Question 49

Confidence intervals for Y may be unreliable when the residuals are not normally distributed.

(True/False)

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Question 50

Which is not a correct way to find the coefficient of determination?

(Multiple Choice)

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Question 51

If SSR = 3600, SSE = 1200, and SST = 4800, then R² is:

(Multiple Choice)

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Question 52

A parsimonious model is one with many weak predictors but a few strong ones.

(True/False)

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Question 53

Non-normality of residuals is not usually considered a major problem unless there are outliers.

(True/False)

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Question 54

Autocorrelation of the residuals may affect the reliability of the t-values for the estimated coefficients of the predictors X₁, X_2,…, X_k.

(True/False)

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Question 55

The effect of a binary predictor is to shift the regression intercept.

(True/False)

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Question 56

Heteroscedasticity exists when all the errors (residuals) have the same variance.

(True/False)

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Question 57

Part of a regression output is provided below. Some of the information has been omitted. Source of variation SS df MS F Regression 3177.17 2 1588.6 Residual 17 17.717 Total 3478.36 19 The approximate value of F is:

(Multiple Choice)

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Question 58

In a regression model of student grades, we would code the nine categories of business courses taken (ACC, FIN, ECN, MGT, MKT, MIS, ORG, POM, QMM) by including nine binary (0 or 1) predictors in the regression.

(True/False)

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Question 59

Non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted Y values.

(True/False)

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Question 60

Which is a characteristic of the variance inflation factor (VIF)?

When autocorrelation is present, the estimates of the coefficients will be unbiased.

Which of the following would be most useful in checking the normality assumption of the errors in a regression model?

In a multiple regression with 3 predictors in a sample of 25 U.S. cities, we would use F_3,21 in a test of overall significance.

Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? 0.499 Adjusted 0.444 91 0.707 9 Std. Error 4.019 Dep. Var. HwyMPG Source SS df MS F p -value Regression 1,305.7251 9 145.0806 8.98 .0000 Residual 1,308.3848 81 16.1529 Total 2,614.1099 90

Which is not a name often given to an independent variable that takes on just two values (0 or 1) according to whether or not a given characteristic is absent or present?

Confidence intervals for Y may be unreliable when the residuals are not normally distributed.

Which is not a correct way to find the coefficient of determination?

If SSR = 3600, SSE = 1200, and SST = 4800, then R² is:

A parsimonious model is one with many weak predictors but a few strong ones.

Non-normality of residuals is not usually considered a major problem unless there are outliers.

Autocorrelation of the residuals may affect the reliability of the t-values for the estimated coefficients of the predictors X₁, X_2,…, X_k.

The effect of a binary predictor is to shift the regression intercept.

Heteroscedasticity exists when all the errors (residuals) have the same variance.

Part of a regression output is provided below. Some of the information has been omitted. Source of variation SS df MS F Regression 3177.17 2 1588.6 Residual 17 17.717 Total 3478.36 19 The approximate value of F is:

In a regression model of student grades, we would code the nine categories of business courses taken (ACC, FIN, ECN, MGT, MKT, MIS, ORG, POM, QMM) by including nine binary (0 or 1) predictors in the regression.

Non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted Y values.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 13: Multiple Regression

Which is a characteristic of the variance inflation factor (VIF)?

When autocorrelation is present, the estimates of the coefficients will be unbiased.

Which of the following would be most useful in checking the normality assumption of the errors in a regression model?

In a multiple regression with 3 predictors in a sample of 25 U.S. cities, we would use F3,21 in a test of overall significance.

Which statement best describes this regression (Y = highway miles per gallon in 91 cars)? 0.499 Adjusted 0.444 91 0.707 9 Std. Error 4.019 Dep. Var. HwyMPG Source SS df MS F p -value Regression 1,305.7251 9 145.0806 8.98 .0000 Residual 1,308.3848 81 16.1529 Total 2,614.1099 90

Which is not a name often given to an independent variable that takes on just two values (0 or 1) according to whether or not a given characteristic is absent or present?

Confidence intervals for Y may be unreliable when the residuals are not normally distributed.

Which is not a correct way to find the coefficient of determination?

If SSR = 3600, SSE = 1200, and SST = 4800, then R2 is:

A parsimonious model is one with many weak predictors but a few strong ones.

Non-normality of residuals is not usually considered a major problem unless there are outliers.

Autocorrelation of the residuals may affect the reliability of the t-values for the estimated coefficients of the predictors X1, X2,…, Xk.

The effect of a binary predictor is to shift the regression intercept.

Heteroscedasticity exists when all the errors (residuals) have the same variance.

Part of a regression output is provided below. Some of the information has been omitted. Source of variation SS df MS F Regression 3177.17 2 1588.6 Residual 17 17.717 Total 3478.36 19 The approximate value of F is:

In a regression model of student grades, we would code the nine categories of business courses taken (ACC, FIN, ECN, MGT, MKT, MIS, ORG, POM, QMM) by including nine binary (0 or 1) predictors in the regression.

Non-normality of the residuals from a regression can best be detected by looking at the residual plots against the fitted Y values.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

In a multiple regression with 3 predictors in a sample of 25 U.S. cities, we would use F_3,21 in a test of overall significance.

If SSR = 3600, SSE = 1200, and SST = 4800, then R² is:

Autocorrelation of the residuals may affect the reliability of the t-values for the estimated coefficients of the predictors X₁, X_2,…, X_k.