Question 1

Test Individual Regression Coefficients for Significance
-A minor league baseball team posted the following data for its 16 best players. Test the significance of the individual predictor variables at $\alpha = 0.05$.

A) Both explanatory variables have a significant linear relationship with the response variable.
B) Consider removing the variable "at bats" because it is not a good predictor of "hits".
C) Consider removing the variable "strikeouts" because it is not a good predictor of "hits".
D) Consider removing both variables because neither is a good predictor of "hits".

Accepted Answer

The answer of Test Individual Regression Coefficients for Significance
-A minor...

Question 2

Determine R^2 and Adjusted R^2
-A minor league baseball team posted the following data for its 16 best players. Determine $\mathrm { R } ^ { 2 }$ for the multiple regression model $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ where $x _ { 1 }$ is At Bats, $x _ { 2 }$ is Strikeouts, and $y ^ { 2 }$ is the response variable "Hits".

A) $99.2 \%$
B) $89.6 \%$
C) $98.9 \%$
D) $99.1 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-A minor league...

Question 3

Determine R^2 and Adjusted R^2
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in his class. He records the number of push ups each student is able to do in 2 minutes, the number of pull ups each student is able to do in 2 minutes, and the time (in seconds) for each student to climb a rope. The data are shown in the table. The teacher wonders whether the number of push ups and the number of pull ups would be good predictors of the time to climb the rope. Determine $\mathrm { R } ^ { 2 }$ for the multiple regression model $\hat { \mathrm { y } } = \mathrm { b } _ { 0 } + \mathrm { b } _ { 1 } \mathrm { x } _ { 1 } + \mathrm { b } _ { 2 } \mathrm { x } _ { 2 }$ where $\mathrm { x } _ { 1 }$ is Push Ups, $\mathrm { x } _ { 2 }$ is Pull Ups, and $\mathrm { y }$ is the response variable "Rope Climb".

A) $86.2 \%$
B) $82.3 \%$
C) $92.8 \%$
D) $64.5 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-A gym teacher...

Question 4

Determine R^2 and Adjusted R^2
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders whether a student's age and GPA would be good predictors of their state board score. She obtains the following data.
Determine $\mathrm { R } ^ { 2 }$ for the multiple regression model $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ where $x _ { 1 }$ is Age, $x _ { 2 }$ is $G P A _ { \text {, and } }$ is the response variable "state board score".

A) $78.1 \%$
B) $73.3 \%$
C) $88.4 \%$
D) $87.9 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-Twelve nursing students...

Question 5

Perform an F-test for Lack of Fit -When performing a multiple linear regression, if we test the null hypothesis that the coefficients are all zero, what is the decision rule? A) If $\mathrm { p } < \alpha$, then reject the null hypothesis. B) If $p > \alpha$, then reject the null hypothesis. C) If $\mathrm { p } < \alpha$, then fail to reject the null hypothesis. D) If $p > \alpha$, then fail to reject the alternative hypothesis.

Accepted Answer

When performing hypothesis testing, if the p-value ($p$) is less than the significance level ($\alpha$), the decision rule is to reject the null hypothesis. This indicates that there is enough evidence to suggest that at least one of the coefficients in the model is significantly different from zero.

Question 6

Perform an F-test for Lack of Fit
-A minor league baseball team posted the following data for its 16 best players. Test the null hypothesis that all coefficients are zero at the $95 \%$ confidence level.

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) The probability plot of residuals indicates non-normality of residuals so the hypothesis test is inconclusive.
D) The probability plot of residuals indicates normality of residuals so the hypothesis test is inconclusive.

Accepted Answer

The answer of Perform an F-test for Lack of Fit
-A...

Question 7

Construct Confidence and Prediction Intervals
-A minor league baseball team posted the following data for its 16 best players. Construct a $95 \%$ prediction interval for the number of hits player will get if the player is at bat 53 times.

A) $( 16.12,43.49 )$
B) $( 26.17,33.43 )$
C) $( 22.49,39.76 )$
D) $( 0.23,62.03 )$

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-A minor league...

Question 8

Construct Confidence and Prediction Intervals
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if there is a correlation between a student's age, their GPA and their state board score. She collects data about the 12 students. The data is given below. Construct a $95 \%$ prediction interval for the State Board Score a student will get if the student's age is 24 .

A) $( 527.93,620.67 )$
B) $( 561.30,587.30 )$
C) $( 542.5,608.6 )$
D) The result is not reliable because the predictor variable is not a good indicator of the State Board Score.

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-Twelve nursing students...

Question 9

Construct Confidence and Prediction Intervals
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in small class. The exercises consist of doing as many push-ups as possible in 2 minutes. After a rest the student does as many push-ups as possible in 2 minutes. After a rest the student climbs a rope and the time is recorded in seconds. The data for this class is given below. Construct a $95 \%$ prediction interval for the Rope Climb Time if the student's Pull-ups are $22 .$

A) The result is not reliable because the predictor variable is not a good indicator of the Rope Climb Time.
B) $( 41.70,64.85 )$
C) $( 47.09,58.45 )$
D) $( 38.89,66.65 )$

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-A gym teacher...

Question 10

Test Individual Regression Coefficients for Significance
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in small class. The exercises consist of doing as many push-ups as possible in 2 minutes. After a rest the student does as many push-ups as possible in 2 minutes. After a rest the student climbs a rope and the time is recorded in seconds. The data for this class is given below. Test the significance of the individual predictor variables at $\alpha = 0.05$.

A) Consider removing the variable "Pull-ups" because it is not a good predictor of "Rope Climb Time".
B) Both explanatory variables have a significant linear relationship with the response variable.
C) Consider removing the variable "Push-ups" because it is not a good predictor of "Rope Climb Time".
D) Consider removing both variables because neither is a good predictor of "Rope Climb Time".

Accepted Answer

The answer of Test Individual Regression Coefficients for Significance
-A gym...

Question 11

Construct Confidence and Prediction Intervals
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in small class. The exercises consist of doing as many push-ups as possible in 2 minutes. After a rest the student does as many push-ups as possible in 2 minutes. After a rest the student climbs a rope and the time is recorded in seconds. The data for this class is given below. Construct a $95 \%$ confidence interval for the Rope Climb Time if the student's Push-ups are $22 .$

A) $( 48.78,57.77 )$
B) $( 41.70,64.85 )$
C) $( 47.09,58.45 )$
D) $( 38.89,66.65 )$

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-A gym teacher...

Question 12

Determine R^2 and Adjusted R^2
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if a student's age and GPA would be good predictors of their state board score. She obtains the following data.
Determine the adjusted $R ^ { 2 }$ for the multiple regression model $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ where $x _ { 1 }$ is Age, $x _ { 2 }$ is GPA, and $y$ is the response variable "state board score".

A) $73.3 \%$
B) $78.1 \%$
C) $82.9 \%$
D) $67.9 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-Twelve nursing students...

Question 13

Determine R^2 and Adjusted R^2
-A minor league baseball team posted the following data for its 16 best players. Determine the adjusted $R 2$ for the multiple regression model $\mathrm { y } = \mathrm { b } _ { 0 } + \mathrm { b } _ { 1 } \mathrm { x } _ { 1 } + \mathrm { b } _ { 2 } \mathrm { x } _ { 2 }$ where $\mathrm { x } _ { 1 }$ is At Bats, $\mathrm { x } _ { 2 }$ is Strikeouts, and $\mathrm { y }$ is the response variable "Hits".

A) $99.1 \%$
B) $99.2 \%$
C) $98.9 \%$
D) $99.3 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-A minor league...

Question 14

Perform an F-test for Lack of Fit
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if there is a correlation between a student's age, their GPA and their state board score. She collects data about the 12 students. The data is given below. Test the null hypothesis that all coefficients are zero at the $95 \%$ confidence level.

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) The probability plot of residuals indicates non-normality of residuals so the hypothesis test is inconclusive.
D) The probability plot of residuals indicates normality of residuals so the hypothesis test is inconclusive.

Accepted Answer

The answer of Perform an F-test for Lack of Fit
-Twelve...

Question 15

Construct Confidence and Prediction Intervals
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if there is a correlation between a student's age, their GPA and their state board score. She collects data about the 12 students. The data is given below. Construct a $95 \%$ confidence interval for the State Board Score a student will get if the student's age is 24 .

A) $( 561.30,587.30 )$
B) $( 527.93,620.67 )$
C) $( 542.5,608.6 )$
D) $( 476.6,674.4 )$

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-Twelve nursing students...

Question 16

Perform an F-test for Lack of Fit
-By saying that we reject the null hypothesis in a hypothesis test of the coefficients of a multiple linear regression we are implying that
A) at least one coefficient is different from zero.
B) all coefficients are different from zero.
C) the relationship is not linear.
D) non-parametric methods must be used on this problem.

Accepted Answer

Rejecting the null hypothesis in a hypothesis test of the coefficients of a multiple linear regression implies that at least one of the coefficients is significantly different from zero, indicating that the corresponding variable has a significant linear relationship with the dependent variable.

Question 17

Determine R^2 and Adjusted R^2
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in his class. He records the number of push ups each student is able to do in 2 minutes, the number of pull ups each student is able to do in 2 minutes, and the time (in seconds) for each student to climb a rope. The data are shown in the table. The teacher wonders whether the number of push ups and the number of pull ups would be good predictors of the time to climb the rope. Determine the adjusted $R ^ { 2 }$ for the multiple regression model $\hat { y } = b _ { 0 } + b _ { 1 } x _ { 1 } + b _ { 2 } x _ { 2 }$ where $x _ { 1 }$ is Push Ups, $x _ { 2 }$ is Pull Ups, and $y$ is the response variable "Rope Climb".

A) $82.3 \%$
B) $86.2 \%$
C) $92.8 \%$
D) $74.5 \%$

Accepted Answer

The answer of Determine R^2 and Adjusted R^2
-A gym teacher...

Question 18

Perform an F-test for Lack of Fit
-A gym teacher uses three exercises to increase arm strength: push-ups, pull-ups, and rope climbing. He has 10 students in small class. The exercises consist of doing as many push-ups as possible in 2 minutes. After a rest the student does as many push-ups as possible in 2 minutes. After a rest the student climbs a rope and the time is recorded in seconds. The data for this class is given below. Test the null hypothesis that all coefficients are zero at the $95 \%$ confidence level.

A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) The probability plot of residuals indicates non-normality of residuals so the hypothesis test is inconclusive.
D) The probability plot of residuals indicates normality of residuals so the hypothesis test is inconclusive.

Accepted Answer

The answer of Perform an F-test for Lack of Fit
-A...

Question 19

Test Individual Regression Coefficients for Significance
-Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if there is a correlation between a student's age, their GPA and their state board score. She collects data about the 12 students. The data is given below. Test the significance of the individual predictor variables at $\alpha = 0.05$.

A) Consider removing the variable "GPA" because it is not a good predictor of "State Board Scores".
B) Both explanatory variables have a significant linear relationship with the response variable.
C) Consider removing the variable "Age" because it is not a good predictor of "State Board Score".
D) Consider removing both variables because neither is a good predictor of"State Board Scores".

Accepted Answer

The answer of Test Individual Regression Coefficients for Significance
-Twelve nursing...

Question 20

Construct Confidence and Prediction Intervals
-A minor league baseball team posted the following data for its 16 best players. Construct a $95 \%$ confidence interval for the number of hits player will get if the player is at bat 53 times.

A) $( 26.17,33.43 )$
B) $( 16.12,43.49 )$
C) $( 22.49,39.76 )$
D) $( 0.23,62.03 )$

Accepted Answer

The answer of Construct Confidence and Prediction Intervals
-A minor league...

Quiz 14: Inference of the Least-Squares Regression Model and Multiple Regression

Test Individual Regression Coefficients for Significance -A minor league baseball team posted the following data for its 16 best players. Test the significance of the individual predictor variables at α=0.05\alpha = 0.05α=0.05 .

Perform an F-test for Lack of Fit -When performing a multiple linear regression, if we test the null hypothesis that the coefficients are all zero, what is the decision rule?

Perform an F-test for Lack of Fit -A minor league baseball team posted the following data for its 16 best players. Test the null hypothesis that all coefficients are zero at the 95%95 \%95% confidence level.

Construct Confidence and Prediction Intervals -A minor league baseball team posted the following data for its 16 best players. Construct a 95%95 \%95% prediction interval for the number of hits player will get if the player is at bat 53 times.

Perform an F-test for Lack of Fit -By saying that we reject the null hypothesis in a hypothesis test of the coefficients of a multiple linear regression we are implying that

Construct Confidence and Prediction Intervals -A minor league baseball team posted the following data for its 16 best players. Construct a 95%95 \%95% confidence interval for the number of hits player will get if the player is at bat 53 times.