Transcript Chapter 16

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
Which of the following assumptions must be added to
the conditions we check in order to make inferences in
simple regression?
A. Quantitative Variable Condition
B. Equal Spread Assumption
C. Linearity Condition
D. Normal Population Assumption
Copyright © 2010 Pearson Education, Inc.
Slide 16- 2
Which of the following assumptions must be added to
the conditions we check in order to make inferences in
simple regression?
A. Quantitative Variable Condition
B. Equal Spread Assumption
C. Linearity Condition
D. Normal Population Assumption
Copyright © 2010 Pearson Education, Inc.
Slide 16- 3
Constructing a scatterplot of residuals against x or
predicted y values can be used to check which of the
following conditions and/or assumptions?
I. Linearity Condition
II. Independence Assumption
III. Equal Variance Assumption
IV. Normal Population Assumption
A. I and II
B. I and III
C. I and IV
D. I, III and IV
Copyright © 2010 Pearson Education, Inc.
Slide 16- 4
Constructing a scatterplot of residuals against x or
predicted y values can be used to check which of the
following conditions and/or assumptions?
I. Linearity Condition
II. Independence Assumption
III. Equal Variance Assumption
IV. Normal Population Assumption
A. I and II
B. I and III
C. I and IV
D. I, III and IV
Copyright © 2010 Pearson Education, Inc.
Slide 16- 5
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?
A. How close the predicted y values are to the estimated
regression line.
B. The spread of points around the estimated regression
line (measured by the residual standard deviation).
C. The sample size.
D. The spread of the x values.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 6
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?
A. How close the predicted y values are to the estimated
regression line.
B. The spread of points around the estimated regression
line (measured by the residual standard deviation).
C. The sample size.
D. The spread of the x values.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 7
Which of the following statements is false
regarding the t-test for the regression slope?
A. The degrees of freedom for the t test statistic are
based on the sample size.
B. β1 = 0 is the null hypothesis.
C. Rejecting the null hypothesis indicates that there is no
significant linear relationship between the two variables.
D. None of the above.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 8
Which of the following statements is false
regarding the t-test for the regression slope?
A. The degrees of freedom for the t test statistic are
based on the sample size.
B. β1 = 0 is the null hypothesis.
C. Rejecting the null hypothesis indicates that there is no
significant linear relationship between the two variables.
D. None of the above.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 9
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 +.965 with a
t-statistic of 5.27 and associated p-value of < .001.
Which of the following is true?
A. There is no significant linear relationship between
campus size and annual sales at the coffee shop.
B. The slope coefficient is significantly different from
zero.
C. The confidence interval for the slope coefficient
contains zero.
D. The correlation between campus size and annual
sales is not significantly different from zero.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 10
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 +.965 with a
t-statistic of 5.27 and associated p-value of < .001.
Which of the following is true?
A. There is no significant linear relationship between
campus size and annual sales at the coffee shop.
B. The slope coefficient is significantly different from
zero.
C. The confidence interval for the slope coefficient
contains zero.
D. The correlation between campus size and annual
sales is not significantly different from zero.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 11
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 -.688 with an associated p-value < .001.
Which of the following its true?
A. There is a significant linear relationship between the
two variables.
B. The estimated slope for the regression line fit using
these data is positive.
C. The correlation is not significantly different from zero.
D. Secretaries with more training make more errors.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 12
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 -.688 with an associated p-value < .001.
Which of the following its true?
A. There is a significant linear relationship between the
two variables.
B. The estimated slope for the regression line fit using
these data is positive.
C. The correlation is not significantly different from zero.
D. Secretaries with more training make more errors.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 13
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 -.697 to -.293. Which
of the following is true?
A. 95% of the errors will decrease between .293 and .697
for each additional hour of training.
B. We are 95% confident that the number of errors
decreases, on average, by between .293 and .697 for
each additional hour of training.
C. We are 95% confident that the number of errors is
between .293 and .697 for all secretaries who are trained.
D. There is no significant relationship between number of
hours of training and number of errors made.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 14
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 -.697 to -.293. Which
of the following is true?
A. 95% of the errors will decrease between .293 and .697
for each additional hour of training.
B. We are 95% confident that the number of errors
decreases, on average, by between .293 and .697 for
each additional hour of training.
C. We are 95% confident that the number of errors is
between .293 and .697 for all secretaries who are trained.
D. There is no significant relationship between number of
hours of training and number of errors made.
Copyright © 2010 Pearson Education, Inc.
Slide 16- 15
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 15.3. Which is the correct interpretation?
A. 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.
B. 95% of the time secretaries will make between 1.8 to
15.3 errors.
C. 95% of the documents will contain 1.8 to 15.3 errors.
D. 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.
Slide 16- 16
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 15.3. Which is the correct interpretation?
A. 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.
B. 95% of the time secretaries will make between 1.8 to
15.3 errors.
C. 95% of the documents will contain 1.8 to 15.3 errors.
D. 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.
Slide 16- 17