A fitted multiple regression equation is Y = 28 + 5X1 - 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as well, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y?

A) Increase by 2 B) Decrease by 4 C) Increase by 4 D) No change in Y A) Increase by 2 B) Decrease by 4 C) Increase by 4 D) No change in Y

If you rerun a regression, omitting a predictor X5, which would be unlikely?

A) The new R2 will decline if X5 was a relevant predictor. B) The new standard error will increase if X5 was a relevant predictor. C) The remaining estimated β's will change if X5 was collinear with other predictors. D) The numerator degrees of freedom for the F test will increase. A) The new R2 will decline if X5 was a relevant predictor. B) The new standard error will increase if X5 was a relevant predictor. C) The remaining estimated β's will change if X5 was collinear with other predictors. D) The numerator degrees of freedom for the F test will increase.

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 SS (residual) is:

A) 3177.17. B) 301.19. C) 17.71. D) impossible to determine. A) 3177.17. B) 301.19. C) 17.71. D) impossible to determine.

The relationship of Y to four other variables was established as Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 5 units and X2 increases 3 units, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y?

A) Decrease by 15 B) Increase by 15 C) No change D) Increase by 5 A) Decrease by 15 B) Increase by 15 C) No change D) Increase by 5

In the following regression, which are the two best predictors? \[\begin{array} { l r r } \hline \text { Variables } & \text { Coefficients } & \text { Std. Error } \\ \hline \text { Intercept } & 9.8080 & 16.9900 \\ \text { NumCyl } & - 1.6804 & 0.5757 \\ \text { HPMax } & - 0.0369 & 0.0140 \\ \text { ManTran } & 0.2868 & 1.2802 \\ \text { Length } & 0.1109 & 0.0601 \\ \text { Wheelbase } & - 0.0701 & 0.1714 \\ \text { Width } & 0.4079 & 0.2922 \\ \text { RearStRm } & - 0.0085 & 0.2018 \\ \text { Weight } & - 0.0025 & 0.0020 \\ \text { Domestic } & - 1.2291 & 1.1391 \\ \hline \end{array}\]

A) NumCyl, HpMax B) Intercept, NumCyl C) NumCyl, Domestic D) ManTran, Width A) NumCyl, HpMax B) Intercept, NumCyl C) NumCyl, Domestic D) ManTran, Width

Exam 13: Multiple Regression

A fitted multiple regression equation is Y = 28 + 5X₁ - 4X₂ + 7X₃ + 2X₄. When X₁ increases 2 units and X₂ increases 2 units as well, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

(Multiple Choice)

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Question 101

The unexplained sum of squares measures variation in the dependent variable Y about the:

(Multiple Choice)

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Question 102

R²_adj can exceed R² if there are several weak predictors.

(True/False)

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Question 103

When multicollinearity is present, the regression model is of no use for making predictions.

(True/False)

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Question 104

If you rerun a regression, omitting a predictor X₅, which would be unlikely?

(Multiple Choice)

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Question 105

A predictor whose pairwise correlation with Y is near zero can still have a significant t-value in a multiple regression when other predictors are included.

(True/False)

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Question 106

The first differences transformation might be tried if autocorrelation is found in a time-series data set.

(True/False)

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Question 107

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 SS (residual) is:

(Multiple Choice)

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Question 108

A multiple regression analysis with two independent variables yielded the following results in the ANOVA table: SS(Total) = 798, SS(Regression) = 738, SS(Error) = 60. The multiple correlation coefficient is:

(Multiple Choice)

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Question 109

The F statistic in a multiple regression is significant if at least one of the predictors has a significant t statistic at a given α.

(True/False)

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Question 110

Does the picture below show strong evidence of heteroscedasticity against the predictor Wheelbase?

(Multiple Choice)

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Question 111

Unlike other predictors, a binary predictor has a t-value that is either 0 or 1.

(True/False)

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Question 112

A logistic regression is appropriate when:

(Multiple Choice)

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Question 113

The relationship of Y to four other variables was established as Y = 12 + 3X₁ - 5X₂ + 7X₃ + 2X₄. When X₁ increases 5 units and X₂ increases 3 units, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

(Multiple Choice)

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Question 114

The t test shows the ratio of an estimated coefficient to its standard error.

(True/False)

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Question 115

In a regression, the model with the best fit is preferred over all other models.

(True/False)

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Question 116

The F statistic and its p-value give a global test of significance for a multiple regression.

(True/False)

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Question 117

In the following regression, which are the two best predictors? Variables Coefficients Std. Error Intercept 9.8080 16.9900 NumCyl -1.6804 0.5757 HPMax -0.0369 0.0140 ManTran 0.2868 1.2802 Length 0.1109 0.0601 Wheelbase -0.0701 0.1714 Width 0.4079 0.2922 RearStRm -0.0085 0.2018 Weight -0.0025 0.0020 Domestic -1.2291 1.1391

(Multiple Choice)

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Question 118

In regression the dependent variable is referred to as the response variable.

(True/False)

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Question 119

Which statement about leverage is incorrect?

(Multiple Choice)

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Question 120

A fitted multiple regression equation is Y = 28 + 5X₁ - 4X₂ + 7X₃ + 2X₄. When X₁ increases 2 units and X₂ increases 2 units as well, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

The unexplained sum of squares measures variation in the dependent variable Y about the:

R²_adj can exceed R² if there are several weak predictors.

When multicollinearity is present, the regression model is of no use for making predictions.

If you rerun a regression, omitting a predictor X₅, which would be unlikely?

A predictor whose pairwise correlation with Y is near zero can still have a significant t-value in a multiple regression when other predictors are included.

The first differences transformation might be tried if autocorrelation is found in a time-series data set.

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 SS (residual) is:

A multiple regression analysis with two independent variables yielded the following results in the ANOVA table: SS(Total) = 798, SS(Regression) = 738, SS(Error) = 60. The multiple correlation coefficient is:

The F statistic in a multiple regression is significant if at least one of the predictors has a significant t statistic at a given α.

Does the picture below show strong evidence of heteroscedasticity against the predictor Wheelbase?

Unlike other predictors, a binary predictor has a t-value that is either 0 or 1.

A logistic regression is appropriate when:

The relationship of Y to four other variables was established as Y = 12 + 3X₁ - 5X₂ + 7X₃ + 2X₄. When X₁ increases 5 units and X₂ increases 3 units, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

The t test shows the ratio of an estimated coefficient to its standard error.

In a regression, the model with the best fit is preferred over all other models.

The F statistic and its p-value give a global test of significance for a multiple regression.

In regression the dependent variable is referred to as the response variable.

Which statement about leverage is incorrect?

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

A fitted multiple regression equation is Y = 28 + 5X1 - 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as well, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y?

The unexplained sum of squares measures variation in the dependent variable Y about the:

R2adj can exceed R2 if there are several weak predictors.

When multicollinearity is present, the regression model is of no use for making predictions.

If you rerun a regression, omitting a predictor X5, which would be unlikely?

A predictor whose pairwise correlation with Y is near zero can still have a significant t-value in a multiple regression when other predictors are included.

The first differences transformation might be tried if autocorrelation is found in a time-series data set.

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 SS (residual) is:

A multiple regression analysis with two independent variables yielded the following results in the ANOVA table: SS(Total) = 798, SS(Regression) = 738, SS(Error) = 60. The multiple correlation coefficient is:

The F statistic in a multiple regression is significant if at least one of the predictors has a significant t statistic at a given α.

Does the picture below show strong evidence of heteroscedasticity against the predictor Wheelbase?

Unlike other predictors, a binary predictor has a t-value that is either 0 or 1.

A logistic regression is appropriate when:

The relationship of Y to four other variables was established as Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 5 units and X2 increases 3 units, while X3 and X4 remain unchanged, what change would you expect in your estimate of Y?

The t test shows the ratio of an estimated coefficient to its standard error.

In a regression, the model with the best fit is preferred over all other models.

The F statistic and its p-value give a global test of significance for a multiple regression.

In regression the dependent variable is referred to as the response variable.

Which statement about leverage is incorrect?

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

A fitted multiple regression equation is Y = 28 + 5X₁ - 4X₂ + 7X₃ + 2X₄. When X₁ increases 2 units and X₂ increases 2 units as well, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?

R²_adj can exceed R² if there are several weak predictors.

If you rerun a regression, omitting a predictor X₅, which would be unlikely?

The relationship of Y to four other variables was established as Y = 12 + 3X₁ - 5X₂ + 7X₃ + 2X₄. When X₁ increases 5 units and X₂ increases 3 units, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y?