1. Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 16: Inference for Regression
Business Statistics First Edition
by Sharpe, De Veaux, Velleman
Copyright © 2010 Pearson Education, Inc.
Slide 10- 1 1

2. Copyright © 2010 Pearson Education, Inc.
Which of the following assumptions must be added to the conditions we check in order to make inferences in simple regression?
Quantitative Variable Condition
Equal Spread Assumption
Linearity Condition
Normal Population Assumption
Copyright © 2010 Pearson Education, Inc.

3. Copyright © 2010 Pearson Education, Inc.
Which of the following assumptions must be added to the conditions we check in order to make inferences in simple regression?
Quantitative Variable Condition
Equal Spread Assumption
Linearity Condition
Normal Population Assumption
Copyright © 2010 Pearson Education, Inc.

4. Copyright © 2010 Pearson Education, Inc.
Constructing a scatterplot of residuals against x or predicted y values can be used to check which of the following conditions and/or assumptions?
Linearity Condition
Independence Assumption
Equal Variance Assumption
Normal Population Assumption
I and II
I and III
I and IV
I, III and IV
Copyright © 2010 Pearson Education, Inc.

5. Copyright © 2010 Pearson Education, Inc.
Constructing a scatterplot of residuals against x or predicted y values can be used to check which of the following conditions and/or assumptions?
Linearity Condition
Independence Assumption
Equal Variance Assumption
Normal Population Assumption
I and II
I and III
I and IV
I, III and IV
Copyright © 2010 Pearson Education, Inc.

6. Copyright © 2010 Pearson Education, Inc.
The standard error of the regression slope indicates how much it varies from sample to sample. Which of the following does not affect the standard error of the slope?
How close the predicted y values are to the estimated regression line.
The spread of points around the estimated regression line (measured by the residual standard deviation).
The sample size.
The spread of the x values.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 6 6

7. Copyright © 2010 Pearson Education, Inc.
The standard error of the regression slope indicates how much it varies from sample to sample. Which of the following does not affect the standard error of the slope?
How close the predicted y values are to the estimated regression line.
The spread of points around the estimated regression line (measured by the residual standard deviation).
The sample size.
The spread of the x values.
Copyright © 2010 Pearson Education, Inc.

8. Copyright © 2010 Pearson Education, Inc.
Which of the following statements is false regarding the t-test for the regression slope?
The degrees of freedom for the t test statistic are based on the sample size.
β1 = 0 is the null hypothesis.
Rejecting the null hypothesis indicates that there is no significant linear relationship between the two variables.
None of the above.
Copyright © 2010 Pearson Education, Inc.

9. Copyright © 2010 Pearson Education, Inc.
Which of the following statements is false regarding the t-test for the regression slope?
The degrees of freedom for the t test statistic are based on the sample size.
β1 = 0 is the null hypothesis.
Rejecting the null hypothesis indicates that there is no significant linear relationship between the two variables.
None of the above.
Copyright © 2010 Pearson Education, Inc.

10. Copyright © 2010 Pearson Education, Inc.
A well known coffee chain locates shops on or near college campuses. Data were collected to determine if campus size and annual sales were related. The estimated slope coefficient was found to be with a t-statistic of 5.27 and associated p-value of < Which of the following is true?
There is no significant linear relationship between campus size and annual sales at the coffee shop.
The slope coefficient is significantly different from zero.
The confidence interval for the slope coefficient contains zero.
The correlation between campus size and annual sales is not significantly different from zero.
Copyright © 2010 Pearson Education, Inc.

11. Copyright © 2010 Pearson Education, Inc.
A well known coffee chain locates shops on or near college campuses. Data were collected to determine if campus size and annual sales were related. The estimated slope coefficient was found to be with a t-statistic of 5.27 and associated p-value of < Which of the following is true?
There is no significant linear relationship between campus size and annual sales at the coffee shop.
The slope coefficient is significantly different from zero.
The confidence interval for the slope coefficient contains zero.
The correlation between campus size and annual sales is not significantly different from zero.
Copyright © 2010 Pearson Education, Inc.

12. Copyright © 2010 Pearson Education, Inc.
A temp agency recently trained its clerical pool in the use of a new version of word processing software. The correlation between the number of hours of training received and the number of errors made in typing a standard document for a sample of 30 secretaries was found to be with an associated p-value < Which of the following its true?
There is a significant linear relationship between the two variables.
The estimated slope for the regression line fit using these data is positive.
The correlation is not significantly different from zero.
Secretaries with more training make more errors.
Copyright © 2010 Pearson Education, Inc.

13. Copyright © 2010 Pearson Education, Inc.
A temp agency recently trained its clerical pool in the use of a new version of word processing software. The correlation between the number of hours of training received and the number of errors made in typing a standard document for a sample of 30 secretaries was found to be with an associated p-value < Which of the following its true?
There is a significant linear relationship between the two variables.
The estimated slope for the regression line fit using these data is positive.
The correlation is not significantly different from zero.
Secretaries with more training make more errors.
Copyright © 2010 Pearson Education, Inc.

14. Copyright © 2010 Pearson Education, Inc.
In the previous example, suppose the temp agency fit a regression equation using these data (x = number of hours of training and y = number of errors). The 95% confidence interval for the slope is to Which of the following is true?
95% of the errors will decrease between .293 and .697 for each additional hour of training.
We are 95% confident that the number of errors decreases, on average, by between .293 and .697 for each additional hour of training.
We are 95% confident that the number of errors is between .293 and .697 for all secretaries who are trained.
There is no significant relationship between number of hours of training and number of errors made.
Copyright © 2010 Pearson Education, Inc.

15. Copyright © 2010 Pearson Education, Inc.
In the previous example, suppose the temp agency fit a regression equation using these data (x = number of hours of training and y = number of errors). The 95% confidence interval for the slope is to Which of the following is true?
95% of the errors will decrease between .293 and .697 for each additional hour of training.
We are 95% confident that the number of errors decreases, on average, by between .293 and .697 for each additional hour of training.
We are 95% confident that the number of errors is between .293 and .697 for all secretaries who are trained.
There is no significant relationship between number of hours of training and number of errors made.
Copyright © 2010 Pearson Education, Inc.

16. Copyright © 2010 Pearson Education, Inc.
Using the estimated regression equation, the temp agency constructs a 95% prediction interval for the number of errors made when x = 6 hours. This interval is 1.8 to Which is the correct interpretation?
We are 95% confident that the mean number of errors made by secretaries receiving 6 hours of training is between 1.8 to 15.3 errors.
95% of the time secretaries will make between 1.8 to 15.3 errors.
95% of the documents will contain 1.8 to 15.3 errors.
We are 95% confident that a secretary who receives 6 hours of training will make between 1.8 to 15.3 errors.
Copyright © 2010 Pearson Education, Inc.

17. Copyright © 2010 Pearson Education, Inc.
Using the estimated regression equation, the temp agency constructs a 95% prediction interval for the number of errors made when x = 6 hours. This interval is 1.8 to Which is the correct interpretation?
We are 95% confident that the mean number of errors made by secretaries receiving 6 hours of training is between 1.8 to 15.3 errors.
95% of the time secretaries will make between 1.8 to 15.3 errors.
95% of the documents will contain 1.8 to 15.3 errors.
We are 95% confident that a secretary who receives 6 hours of training will make between 1.8 to 15.3 errors.
Copyright © 2010 Pearson Education, Inc.