Deck 14: Inference for Regression

Question 1

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
List each of the four conditions for regression and inference and describe whether or
not they are satisfied.

Answer 1

Question 2

Use the following information for questions
Nutritional information was collected for 77 breakfast cereals including the amount of fiber (in grams), potassium (in mg), and the number of calories per serving. The data resulted in the following scatterplots.

Compare the two plots with respect to the aspects that would affect the standard error
of the regression slope?

Answer 2

Question 3

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
Circle the standard error of the slope and its components in the output shown. If the
information is not in the output, list components.

Answer 3

Question 4

Data on labor productivity and unit labor costs were obtained for the retail industry from 1987 through 2006 (Bureau of Labor Statistics). A regression was estimated to describe the linear relationship between the two variables. Based on the plot of residuals versus predicted values, is the linear model appropriate? Explain.

Question 5

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
Is there a significant relationship between time it takes to troubleshoot the process
(minutes) and training received (use α = .05)? Give the appropriate test statistic,
associated P-value, and conclusion.

Question 6

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
The confidence interval and prediction interval for the number of units sold per
month when GPA = 3.00 are shown below. Write a sentence to interpret each
interval in this context.

Question 7

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
What percentage of the variability in sales performance (units sold per month) can be
accounted for by college GPA?

Question 8

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
Predict the units sold per month for a new hire whose college GPA is 3.00.

Question 9

A sales manager claims that there is a relationship between college GPA and sales performance (number of units sold) among salespeople hired within the last year.
Use the regression results are shown below and set α = .05 to test his claim.

A) reject the null hypothesis and conclude that there is no significant relationship
Between GPA and sales performance
B) fail to reject the null hypothesis and conclude that there is no significant
Relationship between GPA and sales performance
C) reject the null hypothesis and conclude that there is a significant relationship
Between GPA and sales performance
D) fail to reject the null hypothesis and conclude that there is a significant
Relationship between GPA and sales performance
E) None of these

Question 10

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
Predict the troubleshooting time for a line worker who received 8 hours of training.

Question 11

The following plots show (1) world population (millions) plotted against 5-year intervals from 1950 through 2000 and (2) residual vs. fitted value for a linear regression model estimated to describe the trend in world population over time. Based on these plots, would you consider this model appropriate? Explain.

Question 12

Use the following information for questions
Nutritional information was collected for 77 breakfast cereals including the amount of fiber (in grams), potassium (in mg), and the number of calories per serving. The data resulted in the following scatterplots.

From which of these plots would you expect a more consistent regression slope estimate? Why?

Question 13

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
According to the data, a worker who received 8 hours of training had a
troubleshooting time of 15 minutes. What is the value of the residual for this worker?
Explain what the residual means.

Question 14

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
From the output, write the equation of the regression equation that can be used to
predict troubleshooting time.

Question 15

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
Based on the scatterplot, what is the relationship between training and troubleshooting? Is a regression appropriate for this data? Why or why not?

Question 16

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
The 95% confidence interval for troubleshooting time with 8 hours of training is
(15.180, 16.903). Interpret this interval with respect to the estimated troubleshooting
time.

Question 17

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
What is the independent variable in this regression? Write the null and alternative
hypothesis to test the slope of this variable.

Question 18

Use the following for questions
An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Below are the scatterplot, regression results, and residual plots for these data.
Write a sentence to interpret the coefficient of training in the regression equation.

Question 19

A sales manager was interested in determining if there is a relationship between college GPA and sales performance (number of units sold) among salespeople hired
Within the last year. The correct null hypothesis is

A) There is no relationship between GPA and sales performance.
B) There is a relationship between GPA and sales performance.
C) β1 = 0
D) Both A and C.
E) None of these

Question 20

Use the following for questions
A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and college GPA and the number of units sold last month recorded. Below are the scatterplot, regression results, and residual plots for these data. Answer:
Test the hypotheses about the slope of the regression line. Give the appropriate test
statistic, associated P-value, and conclusion in terms of the problem.

Question 21

As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types of
Steel. Based on these data he obtained the following regression results, which of the
Following statements is NOT true?

A) The association between carbon content and ductility of steel is statistically
Significant at α = 0.05.
B) The slope is significantly different from zero at α = 0.05.
C) The relationship between carbon content and ductility of steel is positive at α =
0)05.
D) There is 59% of the variance in ductility that is not explained by this model.
E) For one unit increase in carbon content, one can expect a 3.30 unit decrease in
Ductility.

Question 22

Consider Scatterplots 1 and 2 with fitted regression lines shown below. Which of the following statements is true?

A) The standard error of the regression slope is smaller in scatterplot 1.
B) The relationship between x and y is stronger in scatterplot 1.
C) The standard error of the regression slope is smaller in scatterplot 2.
D) The estimated slope is negative in scatterplot 2.
E) The estimated intercept is negative in scatterplot 1.

Question 23

Based on the scatterplot of data of the number of hours of training time received by production line workers and the time it took (in minutes) for them to trouble shoot
Their last process problem shown, we can say that

A) The slope of the regression line fit to these data will be positive.
B) The slope of the regression line fit to these data will be negative.
C) The linearity assumption is not satisfied.
D) The intercept of the regression line fit to these data will be negative.
E) The equal variance assumption is not satisfied.

Question 24

A sales manager was interested in determining if there is a relationship between college GPA and sales performance (number of units sold) among salespeople hired
Within the last year. From the regression results shown below, identify the residual
Standard deviation. S = 1.57429 R-Sq = 78.3% R-Sq(adj) = 76.8%

A) 3.256.
B) 1.044.
C) 1.574.
D) 34.70.
E) None of the above.

Question 25

In a significant regression model determining if there is a relationship between college GPA and sales performance (number of units sold in the previous month), the
95% confidence interval for the number of units sold when GPA = 3.00 was
Determined to be 20.914 to 22.657. The correct interpretation is

A) We can be 95% confident that the number of units sold per month by a particular
Salesperson with a college GPA of 3.00 is between 20.914 and 22.657 units.
B) We can be 95% confident that the average number of units sold per month by
Salespersons with a college GPA of 3.00 is between 20.914 and 22.657 units.
C) The number of units sold per month by a salesperson with a college GPA of 3.00
Will be between 20.914 and 22.657 units 95% of the time.
D) 95% of the time the average number of units sold per month will be between
20)914 and 22.657 units.
E) We can be 95% confident that each month between 20.914 and 22.657 units will
Be sold.

Question 26

Cars from an online service were examined to see how fuel efficiency (highway mpg) relates to cost (in dollars). According to the regression equation, a used car that costs
$13,000 is predicted to get about 30.24 miles per gallon. According to the data, the
Car got 35 miles per gallon. What is the value of the residual for this car?

A) -4.76
B) +1.16
C) +4.76
D) +65.24

Question 27

A sample of recently trained line workers was selected to determine if there is a relationship between the number of hours of training time received by production line
Workers and the time it took (in minutes) for them to trouble shoot their last process
Problem were captured. Using the regression output is shown below, what conclusion
Should be made at α = .05?

A) reject the null hypothesis, there is a significant relationship between amount of
Training received and troubleshooting time
B) do not reject the null hypothesis, , there is a significant relationship between
Amount of training received and troubleshooting time
C) reject the null hypothesis, there is no significant relationship between amount of
Training received and troubleshooting time
D) do not reject the null hypothesis, there is no significant relationship between
Amount of training received and troubleshooting time
E) None of these.

Question 28

When using a plot of residuals (y-axis) vs. fitted value of the dependent variable, a plot with no pattern indicates that the:

A) nearly normal condition is satisfied
B) nearly normal condition is not satisfied
C) equal spread condition is satisfied
D) linearity condition is not satisfied
E) independence condition is not satisfied

Question 29

According to the plot of residuals versus fitted values below, which of the following is true?

A) equal spread condition is satisfied
B) equal spread condition is not satisfied
C) nearly normal condition is not satisfied
D) linearity condition is not satisfied
E) quantitative variables condition is not satisfied

Question 30

A regression equation was fit to the data showing the number of hours of training time received by production line workers and the time it took (in minutes) for them to
Trouble shoot their last process problem and the following histogram of residuals
Obtained. Based on this histogram of the residuals, we can say that the:

A) nearly normal condition is satisfied.
B) nearly normal condition is not satisfied.
C) equal spread condition is satisfied.
D) linearity condition is not satisfied.
E) independence condition is not satisfied.

Question 31

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrolled at his university. Based on his
Regression results, the 95% confidence interval for the slope of the regression
Equation is -0.88 to 1.34. At α = 0.05, we can say

A) There is a statistically significant association between length of essays and SAT
Score.
B) The correlation between length of essays and SAT score is significant.
C) The slope of the regression equation is significantly different from zero.
D) The slope of the regression equation is not significantly different from zero.
E) The relationship between length of essays and SAT scores is significant and
Negative.

Question 32

A researcher is interested in developing a model that can be used to distribute assistance to low income families for food costs. She used data from a national social
Survey to predict weekly amount spent on food using household income (in $1000).
The resulting regression equation is
) How
Much money would be needed to feed a family for a week whose household income
Is $12,000?

A) $9341.33
B) $871.33
C) $193.73
D) $110.57

Question 33

A sample of 15 recently trained line workers was selected to determine if there is a relationship between the number of hours of training time received by production line
Workers and the time it took (in minutes) for them to trouble shoot their last process
Problem were captured. Use the regression output for the independent variable
Shown below to find the 95% confidence interval for the slope of the regression
Equation.

A) -4 to 0.32
B) -1.9776 to -1.7224
C) -2.1332 to -1.5388
D) -3.611 to -0.069
E) Can't be determined with the information given.

Question 34

As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types of
Steel. According to the output provided below, the standard error of the regression
Slope is

A) -3.296
B) +2.363
C) +1.097
D) +1.507
E) +5.090

Question 35

Which of the following does NOT affect the standard error of the regression slope?

A) Spread around the line: se
B) Spread of x values: sx
C) Sample size: n
D) Critical value: t*
E) All of these affect the standard error.

Question 36

An estimated regression equation that was fit to estimate ductility in steel using its carbon content was found to be significant at α = 0.05. The 95% prediction interval
For the ductility of steel with 0.5% carbon content was determined to be 0.45 to 11.59.
The correct interpretation is

A) We can be 95% confident that the ductility of a particular type of steel with 0.5%
Carbon content is between 0.45 and 11.59.
B) We can be 95% confident that the average ductility of all steel with 0.5% carbon
Content is between 0.45 and 11.59.
C) The ductility of steel with 0.5% carbon content will be between 45 and 11.59
Most (95%) of the time.
D) 95% of the time the average ductility of steel with 0.5% carbon content will be
Between 0.45 and 11.59.
E) We can be 95% confident that all steel with have ductility measurements between 0.45 and 11.59.

Question 37

As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types ofsteel. Use the following regression results to find the 95% confidence interval for the
Slope of the regression equation.

A) -5.456 to -1.136
B) -4.393 to -2.199
C) 6.164 to 9.178
D) -5.666 to -0.926
E) 2.581 to 12.761

Question 38

The number of hours of training time received by employees and the time it took (in minutes) for them to trouble shoot their last process problem was estimated using a
Regression equation. The 95% prediction interval for trouble shooting time with 8
Hours of training was determined to be 12.822 to 19.261. The correct interpretation is

A) We can be 95% confident that the trouble shooting time by a particular line
Worker who received 8 hours of training will be between 12.822 and 19.261
Minutes.
B) We can be 95% confident that the average trouble shooting time by line workers
Receiving 8 hours of training is between 12.822 and 19.261 minutes.
C) The troubleshooting time by a line worker who received 8 hours of training will
Be between 12.822 and 19.261 minutes 95% of the time.
D) 95% of the time the average troubleshooting time is between 12.822 and 19.261
Minutes.
E) We can be 95% confident that troubleshooting times will be between 12.822 and 19.261 minutes.