2. The data set prostate in the faraway package is from a study on 97 men with prostate cancer who were due to receive a radical prostatectomy. We are interest is in predicting Ipsa (log prostate specific antigen) with Icavol (log cancer volume). (a) Draw a scatterplot - does a simple linear regression model seem reasonable? (b) Without using the R function Im(), compute the values z, Y, Sxx, Syy and Sxy. Com- pute the ordinary least squares estimates of the intercept and slope for the simple linear regression model, and draw the fitted line on your plot from part (a). (c) Obtain the estimate of o2 and find the estimated standard errors of Bo and 3. (d) Find the estimated covariance between Bo and 3. (e) Carry out t-tests for the two null hypotheses Bo = 0 and 3 = 0, reporting the value of the test statistic and a p-value in each case. (f) Use the R. function Im() to fit the regressions of lpsa on lcavol.