STA 403 Name:

HW3

Please complete the following problems. Remember to adhere to the homework guidelines described in the course syllabus.

Problem 3.6 - uses Plastic hardness data (CH01PR22) described on text p. 36. (10 pts)

Store the residuals in Minitab and use them to construct a box plot. What information is provided by your plot? (3)

Plot the residuals against the fitted values  to ascertain whether any departures from the normal errors SLR model are evident. State your findings. (3)

Prepare a P-P plot of the residuals. Conduct the Ryan-Joiner test for normality of the residuals. State the hypotheses, p-value, and conclusion. (4)

Problem 3.10 – uses Per capita earnings data (CH03PR10). A sociologist employed the normal

errors SLR model to relate per capita earnings () to average number of years of schooling ()

for 12 cities. The fitted values  and the standardized residuals follow. (6 pts)

Obtain Minitab’s “standardized residuals” and plot them against the fitted values. What does the plot suggest? (3)

How many standardized residuals are outside standard deviation? Approximately how many would you expect to see if the normal error model is appropriate? Recall the 68-95-99.7 rule for normal distributions. (3)

Problem 3.11 – uses the Drug concentration data (CH03PR11). A pharmacologist employed the normal errors SLR model to study the relation between the concentration of a drug in plasma () and the log-dose of the drug (). The residuals and log-dose levels follow. (8 pts)

Plot the residuals against . What conclusions do you draw from the plot? (3)

Assume that the following statement is applicable:

and conduct the Breusch-Pagan test to determine whether the error variance is related to log-dose of the drug. Use . State the hypotheses, decision rule, and conclusion. Does your conclusion support your preliminary findings in part (a)? (5)

Problem 3.16 – uses the Solution concentration data (CH03PR15). (16 pts)

Prepare a scatter plot of the original data, vs . Also apply the transformation

and present a scatter plot of vs . (3)

Use the Box-Cox procedure in Minitab to find the “optimal” value of . State the value of when fitting a model based on the transformed version of (using the optimal ). (4)

Use the transformation and obtain the estimated linear regression function for the transformed data. (2)

Plot the estimated regression line and the transformed data. Does the regression line appear to be a good fit to the transformed data? (3)

Obtain the residuals and plot them against the fitted values. Also prepare a P-P plot. What do your plots show? (4)

Problem 3.18 – uses the Production time data (CH03PR18). In a manufacturing study, the production time for 111 recent production runs were obtained. The table below lists for each run the production time in hours () and the production lot size (). (10 pts)

Prepare a scatter plot of the data. Does a linear relation appear adequate here? Would a transformation on or be more appropriate here? Why? (3)

Use the transformation and obtain the estimated linear regression function for the transformed data. (1)

Plot the estimated regression line and the transformed data. Does the regression line appear to be a good fit to the transformed data? (2)

Obtain the residuals and plot them against the fitted values. Also prepare a P-P plot. What do your plots show? (4)