 Regression Analysis Questions

Subject Mathematics General Statistics

Question

1. (Data source: Applied Linear Statistical Models, 5th Ed., by Kutner, Nachtsheim, Neter, and Li, McGraw-Hill, 2005) An office equipment corporation performs preventive maintenance and repair on the line of copies that it sells. For 45 recent service calls data has been collected on the number of copiers serviced during the call and the number of minutes spent on the call by the service person. The company would like to develop a regression model that can be used to predict the amount of time (in minutes) that a call will require based on the number of copiers that need to be serviced. The data file for this problem can be found with your assignment.

(a) Find the equation for the estimated least-squares regression line. Report your fitted equation along with t-stats, the F-stat, R-squared values and ANOVA table. (For example you can paste in a Minitab regression printout from the beginning through the ANOVA table.) Then plot both the data points and the sample regression line on the same plot.

(b) Plot the residuals vs. fitted values. Based on the plot, do you believe that the assumptions of the regression model hold? Is the model a good fit?

(c) Perform a formal test to check the assumption of normally distributed error terms. Use level of significance α = 0.05.

(d) Test for a significant linear relation. In other words, test to see if the data provide evidence of a relation between the time spent on a call and the number of copiers serviced. Use level of significance α = 0.05. Perform the test using both a critical value approach and a p-value approach.

(e) Interpret the value of the sample slope in the context of this problem.

(f) Find a 95% confidence interval for the population slope.

(g) Report and interpret the value of the coefficient of determination R2. Also calculate the value of the correlation coefficient r.

(h) Find a 95% confidence interval for the mean time spent on service calls for calls that involve 7 copiers.

(i)
(a) The first service call scheduled for tomorrow involves servicing 5 copiers. Predict, with a .95 probability of being correct, the time that will be required for this service call. Note that to have a .95 probability of being correct, you need to use a PI, not a point predictor.

(b) Repeat (a) but now assume that the call involves servicing 13 copiers rather than 5 copiers.

(c) What key assumption is made when doing the prediction requested in (b) that is not necessary for the prediction requested in (a)?

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