The data used in Example 43 arc taken from the data set given in DS 12.11.2, which relates the variable % scrap to the number of times that the metal plate is passed through the rollers. It is useful to be able to model the amount of discarded metal. 95 scrap, as a function of the number of passes through the rollers. Perform a linear regression analysis with % scrap as the dependent variable and the number of passes through the rollers as the explanatory variable.
(a) Fit the regression line and estimate the error variance.
(b) Calculate the sample correlation coefficient r-.
(c) What is the evidence that the amount of scrap material depends upon the number of passes?
(d) Calculate a two-sided 95% confidence interval for the slope parameter B\.
(e) I low does the predicted amount of scrap change with each extra pass through the rollers?
(f) What is the predicted amount of scrap after seven passes through the rollers'.' Construct a two-sided
9595 prediction interval for the amount of scrap after seven passes of a particular sheet through the rollers.
(g) Plot the residuals against the number of passes. Which points have values ei/d larger than 3 in absolute value? Do you think that a straight line regression model is appropriate? Obtain a normal scores plot of the residuals.