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Deck 16: Inference for Regression
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Question
Interpret regression output.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the residual standard
Deviation is
A) 3.256
B) 1.044
C) 1.574
D) 34.70
E) None of the above.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the residual standard
Deviation is
A) 3.256
B) 1.044
C) 1.574
D) 34.70
E) None of the above.
Question
Question
Interpret a scatterplot.
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 trouble shoot 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 trouble shoot their last process problem were captured. Based on the
Scatterplot of the data shown below, 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.
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 trouble shoot 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 trouble shoot their last process problem were captured. Based on the
Scatterplot of the data shown below, 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
Create a confidence interval for the slope of a regression equation.
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.
The 95% confidence interval for the slope of the regression equation is
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
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.
The 95% confidence interval for the slope of the regression equation is
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
Question
Create a confidence interval for the slope of a regression equation.
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 trouble shoot a process problem. A sample of 15 recently trained line workers was
Selected. The number of hours of training time received and the time it took (in minutes)
For them to trouble shoot their last process problem were captured. The regression output
Is shown below. The 95% confidence interval for the slope of the regression equation is
A) -4 to 0.32
B) -1.9776 to -1.7224
C) -2.1332 to -1.5388
D) -3.611 to -0.069
E) None of the above.
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 trouble shoot a process problem. A sample of 15 recently trained line workers was
Selected. The number of hours of training time received and the time it took (in minutes)
For them to trouble shoot their last process problem were captured. The regression output
Is shown below. The 95% confidence interval for the slope of the regression equation is
A) -4 to 0.32
B) -1.9776 to -1.7224
C) -2.1332 to -1.5388
D) -3.611 to -0.069
E) None of the above.
Question
Interpret regression output.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the percentage of
Variability in sales performance (units sold per month) accounted for by college GPA is
A) 50.56%.
B) 78.3%.
C) 34.70%.
D) 100%
E) None of the above.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the percentage of
Variability in sales performance (units sold per month) accounted for by college GPA is
A) 50.56%.
B) 78.3%.
C) 34.70%.
D) 100%
E) None of the above.
Question
Question
Question
The confidence interval and prediction interval for trouble shooting time with 8 hours
of training are shown below. Interpret both intervals in this context.
of training are shown below. Interpret both intervals in this context.
Question
Question
Question
Question
Question
Check assumptions / conditions for inferences in regression.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following residual plot obtained. Based on this plot, we can
Say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following residual plot obtained. Based on this plot, we can
Say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
Question
Check assumptions / conditions for inferences in regression.
Based on the plot of residuals versus fitted values below, we can say that
A) all conditions for inferences in regression are satisfied.
B) the equal spread condition is not satisfied.
C) the linearity condition is not satisfied.
D) the nearly normal condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Based on the plot of residuals versus fitted values below, we can say that
A) all conditions for inferences in regression are satisfied.
B) the equal spread condition is not satisfied.
C) the linearity condition is not satisfied.
D) the nearly normal condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Question
Question
Question
Question
Check assumptions / conditions for inferences in regression.
Based on the plot of residuals versus fitted values below, we can say that
A) the equal spread condition is satisfied.
B) the equal spread condition is not satisfied.
C) the nearly normal condition is not satisfied.
D) the linearity condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Based on the plot of residuals versus fitted values below, we can say that
A) the equal spread condition is satisfied.
B) the equal spread condition is not satisfied.
C) the nearly normal condition is not satisfied.
D) the linearity condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Question
Check assumptions / conditions for inferences in regression.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following histogram of residuals obtained. Based on this
Histogram we can say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following histogram of residuals obtained. Based on this
Histogram we can say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
Question
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Deck 16: Inference for Regression
1
Interpret regression output.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the residual standard
Deviation is
A) 3.256
B) 1.044
C) 1.574
D) 34.70
E) None of the above.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the residual standard
Deviation is
A) 3.256
B) 1.044
C) 1.574
D) 34.70
E) None of the above.
C
2
Interpret a confidence interval for the slope of a regression equation.
A researcher decides to investigate his students' suspicions that longer essays receive
Better scores on the SAT exam. He 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.
A researcher decides to investigate his students' suspicions that longer essays receive
Better scores on the SAT exam. He 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.
D
3
Interpret a scatterplot.
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 trouble shoot 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 trouble shoot their last process problem were captured. Based on the
Scatterplot of the data shown below, 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.
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 trouble shoot 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 trouble shoot their last process problem were captured. Based on the
Scatterplot of the data shown below, 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.
B
4
Create a confidence interval for the slope of a regression equation.
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.
The 95% confidence interval for the slope of the regression equation is
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
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.
The 95% confidence interval for the slope of the regression equation is
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
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5
Test for association.
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
Resulting in a correlation of -0.640. The calculated value of the t-statistic to test for a
Significant association between carbon content and ductility is
A) -3.01
B) 4.692
C) -4.692
D) 5.09
E) 2.363
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
Resulting in a correlation of -0.640. The calculated value of the t-statistic to test for a
Significant association between carbon content and ductility is
A) -3.01
B) 4.692
C) -4.692
D) 5.09
E) 2.363
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6
Create a confidence interval for the slope of a regression equation.
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 trouble shoot a process problem. A sample of 15 recently trained line workers was
Selected. The number of hours of training time received and the time it took (in minutes)
For them to trouble shoot their last process problem were captured. The regression output
Is shown below. The 95% confidence interval for the slope of the regression equation is
A) -4 to 0.32
B) -1.9776 to -1.7224
C) -2.1332 to -1.5388
D) -3.611 to -0.069
E) None of the above.
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 trouble shoot a process problem. A sample of 15 recently trained line workers was
Selected. The number of hours of training time received and the time it took (in minutes)
For them to trouble shoot their last process problem were captured. The regression output
Is shown below. The 95% confidence interval for the slope of the regression equation is
A) -4 to 0.32
B) -1.9776 to -1.7224
C) -2.1332 to -1.5388
D) -3.611 to -0.069
E) None of the above.
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7
Interpret regression output.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the percentage of
Variability in sales performance (units sold per month) accounted for by college GPA is
A) 50.56%.
B) 78.3%.
C) 34.70%.
D) 100%
E) None of the above.
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 the number of units each sold last
Month recorded. Based on the regression results shown below, the percentage of
Variability in sales performance (units sold per month) accounted for by college GPA is
A) 50.56%.
B) 78.3%.
C) 34.70%.
D) 100%
E) None of the above.
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8
Are the assumptions / conditions for regression and inference satisfied? Explain.
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9
What percentage of the variability in sales performance (units sold per month) can be
accounted for by college GPA?
accounted for by college GPA?
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10
The confidence interval and prediction interval for trouble shooting time with 8 hours
of training are shown below. Interpret both intervals in this context.
of training are shown below. Interpret both intervals in this context.
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11
Is there a significant relationship between sales performance (units sold per month)
and college GPA (use α = .05)? Give the appropriate test statistic, associated P-value and
conclusion.
and college GPA (use α = .05)? Give the appropriate test statistic, associated P-value and
conclusion.
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12
Predict the units sold per month for a new hire whose college GPA is 3.00.
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13
Is there a significant relationship between time it takes to trouble shoot the process
(minutes) and training received (use α = .05)? Give the appropriate test statistic,
associated P-value and conclusion.
(minutes) and training received (use α = .05)? Give the appropriate test statistic,
associated P-value and conclusion.
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14
Are the assumptions / conditions for regression and inference satisfied? Explain.
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15
Check assumptions / conditions for inferences in regression.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following residual plot obtained. Based on this plot, we can
Say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following residual plot obtained. Based on this plot, we can
Say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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16
Check assumptions / conditions for inferences in regression.
Based on the plot of residuals versus fitted values below, we can say that
A) all conditions for inferences in regression are satisfied.
B) the equal spread condition is not satisfied.
C) the linearity condition is not satisfied.
D) the nearly normal condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Based on the plot of residuals versus fitted values below, we can say that
A) all conditions for inferences in regression are satisfied.
B) the equal spread condition is not satisfied.
C) the linearity condition is not satisfied.
D) the nearly normal condition is not satisfied.
E) the quantitative variables condition is not satisfied.
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17
Write the null and alternative hypothesis.
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18
Interpret confidence and prediction intervals.
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 trouble shoot 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 trouble shoot their last process problem were captured. The estimated
Regression equation fit to the data was found to be significant at α = 0.05. 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 19.261 minutes.
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
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 trouble shoot 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 trouble shoot their last process problem were captured. The estimated
Regression equation fit to the data was found to be significant at α = 0.05. 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 19.261 minutes.
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
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19
Predict the trouble shooting time for a line worker who received 8 hours of training.
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20
Check assumptions / conditions for inferences in regression.
Based on the plot of residuals versus fitted values below, we can say that
A) the equal spread condition is satisfied.
B) the equal spread condition is not satisfied.
C) the nearly normal condition is not satisfied.
D) the linearity condition is not satisfied.
E) the quantitative variables condition is not satisfied.
Based on the plot of residuals versus fitted values below, we can say that
A) the equal spread condition is satisfied.
B) the equal spread condition is not satisfied.
C) the nearly normal condition is not satisfied.
D) the linearity condition is not satisfied.
E) the quantitative variables condition is not satisfied.
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21
Check assumptions / conditions for inferences in regression.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following histogram of residuals obtained. Based on this
Histogram we can say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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 trouble shoot 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 trouble shoot their last process problem were captured. A regression equation
Was fit to the data and the following histogram of residuals obtained. Based on this
Histogram we can say
A) that the nearly normal condition is satisfied.
B) that the nearly normal condition is not satisfied.
C) that the equal spread condition is satisfied.
D) that the linearity condition is not satisfied.
E) that the independence condition is not satisfied.
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22
Interpret confidence and prediction intervals.
A sales manager was interested in determining if there is a relationship between
College GPA and sales performance (number of units sold in the previous month) among
Salespeople hired within the last year. The estimated regression equation fit to the data
Was found to be significant at α = 0.05. 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
A sales manager was interested in determining if there is a relationship between
College GPA and sales performance (number of units sold in the previous month) among
Salespeople hired within the last year. The estimated regression equation fit to the data
Was found to be significant at α = 0.05. 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
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