The ScamMore Energy Company is attempting to predict natural gas consumption for the month of January. A random sample of 50 homes was used to fit a regression of gas usage (in CCF) using as predictors Temperature = the thermostat setting (degrees Fahrenheit) and Occupants = the number of household occupants. They obtained the following results: \[\begin{array} { l c c } \text { Variable } & \text { Coefficient } & \text { Std Err } \\ \text { Intercept } & 21.684 & 4.122 \\ \text { Temperature } & 0.9142 & 0.2918 \\ \text { Occupants } & 2.244 & 1.315 \end{array}\] In testing each coefficient for a significant difference from zero (two-tailed test at ? = .10), which is the most reasonable conclusion about the predictors?

A) Temperature is highly significant; Occupants is barely significant. B) Temperature is not significant; Occupants is significant. C) Temperature is less significant than Occupants. D) Temperature is significant; Occupants is not significant. A) Temperature is highly significant; Occupants is barely significant. B) Temperature is not significant; Occupants is significant. C) Temperature is less significant than Occupants. D) Temperature is significant; Occupants is not significant.

Refer to this ANOVA table from a regression: \[\begin{array} { l r r r r } \hline \text { Source } & d f & \text { SS } & M S & F \\ \hline \text { Regression } & 4 & 1793.2356 & 448.3089 & 7.48540 \\ \text { Residual } & 45 & 2695.0996 & 59.8911 & \\ \text { Total } & 49 & 4488.3352 & & \\ \hline \end{array}\] Which statement is not accurate?

A) The F-test is significant at ? = .05. B) There were 50 observations. C) There were 5 predictors. D) There would be 50 residuals. A) The F-test is significant at ? = .05. B) There were 50 observations. C) There were 5 predictors. D) There would be 50 residuals.

Refer to this ANOVA table from a regression: \[\begin{array} { l r r r r } \hline \text { Source } & d f & \text { SS } & M S & F \\ \hline \text { Regression } & 4 & 1793.2356 & 448.3089 & 7.48540 \\ \text { Residual } & 45 & 2695.0996 & 59.8911 & \\ \text { Total } & 49 & 4488.3352 & & \\ \hline \end{array}\] For this regression, the R2 is:

A) .3995. B) .6005. C) .6654. D) .8822. A) .3995. B) .6005. C) .6654. D) .8822.

For a given set of values for x1, x2, …, xk the confidence interval for the conditional mean of Y is:

A) narrower than the prediction interval for the individual Y value. B) wider than the prediction interval for the individual Y value. C) usually about the same as the prediction interval for the individual Y value. A) narrower than the prediction interval for the individual Y value. B) wider than the prediction interval for the individual Y value. C) usually about the same as the prediction interval for the individual Y value.

Using a sample of 63 observations, a dependent variable Y is regressed against two variables X1 and X2 to obtain the fitted regression equation Y = 76.40 - 6.388X1 + 0.870X2. The standard error of b1 is 3.453 and the standard error of b2 is 0.611. At α = .05, we could:

A) conclude that both coefficients differ significantly from zero. B) reject H0: β1 ≥ 0 and conclude H0: β1 0: β2 ≤ 0 and conclude H0: β1 > 0. D) conclude that Evans' Rule has been violated. A) conclude that both coefficients differ significantly from zero. B) reject H0: β1 ≥ 0 and conclude H0: β1 0: β2 ≤ 0 and conclude H0: β1 > 0. D) conclude that Evans' Rule has been violated.

If X2 is a binary predictor in Y = β0 + β1X1 + β2X2, then which statement is most nearly correct?

A) X2 = 1 should represent the most desirable condition. B) X2 would be a significant predictor if β2 = 423.72. C) X2 = 0, X2 = 1, X2 = 2 would be appropriate if three categories exist. D) X2 will shift the estimated equation either by 0 units or by β2 units. A) X2 = 1 should represent the most desirable condition. B) X2 would be a significant predictor if β2 = 423.72. C) X2 = 0, X2 = 1, X2 = 2 would be appropriate if three categories exist. D) X2 will shift the estimated equation either by 0 units or by β2 units.

Exam 13: Multiple Regression

The ScamMore Energy Company is attempting to predict natural gas consumption for the month of January. A random sample of 50 homes was used to fit a regression of gas usage (in CCF) using as predictors Temperature = the thermostat setting (degrees Fahrenheit) and Occupants = the number of household occupants. They obtained the following results: Variable Coefficient Std Err Intercept 21.684 4.122 Temperature 0.9142 0.2918 Occupants 2.244 1.315 In testing each coefficient for a significant difference from zero (two-tailed test at ? = .10), which is the most reasonable conclusion about the predictors?

(Multiple Choice)

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Question 61

Given that the fitted regression is Y = 76.40 - 6.388X₁ + 0.870X₂, the standard error of b₁ is 1.453, and n = 63, at α = .05, we can conclude that X₁ is a significant predictor of Y.

(True/False)

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Question 62

A regression with 72 observations and 9 predictors violates:

(Multiple Choice)

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Question 63

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 Which statement is not accurate?

(Multiple Choice)

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Question 64

A widening pattern of residuals as X increases would suggest heteroscedasticity.

(True/False)

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Question 65

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 For this regression, the R² is:

(Multiple Choice)

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Question 66

A large VIF (e.g., 10 or more) would indicate multicollinearity.

(True/False)

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Question 67

Refer to the following correlation matrix that was part of a regression analysis. The dependent variable was 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. Correlation Matrix Abort EdSpend Age Unmar InfMor Abort 1.0000 EdSpend 0.2626 1.0000 Age 0.1610 -0.0420 1.0000 Unmar 0.3286 -0.0949 0.0937 1.0000 InfMor -0.2513 -0.2826 0.0389 0.5239 1.0000 Using a two-tailed correlation test, which statement is not accurate?

(Multiple Choice)

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Question 68

Evans' Rule says that if n = 50 you need at least 5 predictors to have a good model.

(True/False)

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Question 69

Which of the following is not a characteristic of the F distribution?

(Multiple Choice)

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Question 70

In a multiple regression, which is an incorrect statement about the residuals?

(Multiple Choice)

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Question 71

Which estimated multiple regression contains an interaction term?

(Multiple Choice)

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Question 72

A negative estimated coefficient in a regression usually indicates a weak predictor.

(True/False)

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Question 73

There is one residual for each predictor in the regression model.

(True/False)

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Question 74

For a given set of values for x₁, x₂, …, x_k the confidence interval for the conditional mean of Y is:

(Multiple Choice)

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Question 75

Using a sample of 63 observations, a dependent variable Y is regressed against two variables X₁ and X₂ to obtain the fitted regression equation Y = 76.40 - 6.388X₁ + 0.870X₂. The standard error of b₁ is 3.453 and the standard error of b₂ is 0.611. At α = .05, we could:

(Multiple Choice)

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Question 76

In the fitted regression Y = 12 + 3X₁ - 5X₂ + 27X₃ + 2X₄ the most significant predictor is X₃.

(True/False)

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Question 77

Which estimated multiple regression contains an interaction term?

(Multiple Choice)

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Question 78

Which Excel function will give the p-value for overall significance if a regression has 75 observations and 5 predictors and gives an F test statistic F_calc = 3.67?

(Multiple Choice)

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Question 79

If X₂ is a binary predictor in Y = β₀ + β₁X₁ + β₂X₂, then which statement is most nearly correct?

(Multiple Choice)

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Question 80

Given that the fitted regression is Y = 76.40 - 6.388X₁ + 0.870X₂, the standard error of b₁ is 1.453, and n = 63, at α = .05, we can conclude that X₁ is a significant predictor of Y.

A regression with 72 observations and 9 predictors violates:

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 Which statement is not accurate?

A widening pattern of residuals as X increases would suggest heteroscedasticity.

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 For this regression, the R² is:

A large VIF (e.g., 10 or more) would indicate multicollinearity.

Evans' Rule says that if n = 50 you need at least 5 predictors to have a good model.

Which of the following is not a characteristic of the F distribution?

In a multiple regression, which is an incorrect statement about the residuals?

Which estimated multiple regression contains an interaction term?

A negative estimated coefficient in a regression usually indicates a weak predictor.

There is one residual for each predictor in the regression model.

For a given set of values for x₁, x₂, …, x_k the confidence interval for the conditional mean of Y is:

Using a sample of 63 observations, a dependent variable Y is regressed against two variables X₁ and X₂ to obtain the fitted regression equation Y = 76.40 - 6.388X₁ + 0.870X₂. The standard error of b₁ is 3.453 and the standard error of b₂ is 0.611. At α = .05, we could:

In the fitted regression Y = 12 + 3X₁ - 5X₂ + 27X₃ + 2X₄ the most significant predictor is X₃.

Which estimated multiple regression contains an interaction term?

Which Excel function will give the p-value for overall significance if a regression has 75 observations and 5 predictors and gives an F test statistic F_calc = 3.67?

If X₂ is a binary predictor in Y = β₀ + β₁X₁ + β₂X₂, then which statement is most nearly correct?

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

Given that the fitted regression is Y = 76.40 - 6.388X1 + 0.870X2, the standard error of b1 is 1.453, and n = 63, at α = .05, we can conclude that X1 is a significant predictor of Y.

A regression with 72 observations and 9 predictors violates:

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 Which statement is not accurate?

A widening pattern of residuals as X increases would suggest heteroscedasticity.

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 For this regression, the R2 is:

A large VIF (e.g., 10 or more) would indicate multicollinearity.

Evans' Rule says that if n = 50 you need at least 5 predictors to have a good model.

Which of the following is not a characteristic of the F distribution?

In a multiple regression, which is an incorrect statement about the residuals?

Which estimated multiple regression contains an interaction term?

A negative estimated coefficient in a regression usually indicates a weak predictor.

There is one residual for each predictor in the regression model.

For a given set of values for x1, x2, …, xk the confidence interval for the conditional mean of Y is:

Using a sample of 63 observations, a dependent variable Y is regressed against two variables X1 and X2 to obtain the fitted regression equation Y = 76.40 - 6.388X1 + 0.870X2. The standard error of b1 is 3.453 and the standard error of b2 is 0.611. At α = .05, we could:

In the fitted regression Y = 12 + 3X1 - 5X2 + 27X3 + 2X4 the most significant predictor is X3.

Which estimated multiple regression contains an interaction term?

Which Excel function will give the p-value for overall significance if a regression has 75 observations and 5 predictors and gives an F test statistic Fcalc = 3.67?

If X2 is a binary predictor in Y = β0 + β1X1 + β2X2, then which statement is most nearly correct?

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

Given that the fitted regression is Y = 76.40 - 6.388X₁ + 0.870X₂, the standard error of b₁ is 1.453, and n = 63, at α = .05, we can conclude that X₁ is a significant predictor of Y.

Refer to this ANOVA table from a regression: Source df SS MS F Regression 4 1793.2356 448.3089 7.48540 Residual 45 2695.0996 59.8911 Total 49 4488.3352 For this regression, the R² is:

For a given set of values for x₁, x₂, …, x_k the confidence interval for the conditional mean of Y is:

Using a sample of 63 observations, a dependent variable Y is regressed against two variables X₁ and X₂ to obtain the fitted regression equation Y = 76.40 - 6.388X₁ + 0.870X₂. The standard error of b₁ is 3.453 and the standard error of b₂ is 0.611. At α = .05, we could:

In the fitted regression Y = 12 + 3X₁ - 5X₂ + 27X₃ + 2X₄ the most significant predictor is X₃.

Which Excel function will give the p-value for overall significance if a regression has 75 observations and 5 predictors and gives an F test statistic F_calc = 3.67?

If X₂ is a binary predictor in Y = β₀ + β₁X₁ + β₂X₂, then which statement is most nearly correct?