The Toluca Company manufacturers refrigeration equipment and replacement parts. One particular part is made in lots of various sizes, and the company is interested in learning about the relationship between the size of the lot and the number of hours needed to produce the lot. The company would like to use the lot size to predict the number of hours needed. (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 lot size and the time to produce the lot. 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 a lot that involves 70 parts.
(i) (a) This week a lot of 80 parts will be produced. Predict, with a .95 probability of being correct, the number of work hours that will be needed. 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 lot size is 150 rather than 80.
(c) What key assumption is made when doing the prediction requested in (b) that is not necessary for the prediction requested in (a)?
Lot_Size Work_Hours
80
399
30
121
50
221
90
376
70
361
60
224
120
546
80
352
100
353
50
157
40
160
70
252
90
389
20
113
110
435
100
420
30
212
50
268
90
377
110
421
30
273
90
468
40
244
80
342
70
323