2. The data set prostate in the faraway package is from a study of 9'? men with prostate canoer. Interest is in predicting 1psa (log prostate specic antigen) with loavol {log cancer volume]. [a] Dray.r a scatterth - does a simple linear regression model seem reasonable? (b) Without using the function In, compute the values :3, 17', Sxx: Sn.- and Sxy. Compute the ordinary least squsres estimates of the intercept and slope for the simple linear regression model, and draw the tted line on your plot from part a). [c] Obtain the estimate of o2 and nd the estimated standard errors of 3.3, and 51- Also nd the estimated covariance between these two estimates. Carry out ttests for the two null hypotheses .80 = I] and ,31 = , reporting the 1Iralue of the tilt statistic and a pyalue in each case