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The elecin'c power consumed each month bv a chemical plant is thought to be related to the average ambient temperature 11, the number of days in the month :2, the average product purity:r x3, and the tons of product produced 14. The past vear's historical data are available and are presented in the following table. 9 35 3E 3% 3M 249 25 24 91 199 235 31 21 99 95 299 45 24 33 1 19 224 59 25 ST 55 391 55 25 91 94 315 7'2 25 94 99 399 59 25 ST 9? 295 54 25 95 95 25? 7'5 24 SS 1 19 2'75 59 25 91 195 288 59 25 99 199 251 33 23 S9 98 {a} Fit a multiple linear regression model using the above data set. {b} Predict power consumption fora month in which x1 = T5\" F, x2 = 24 days, 13 = 90%, and x4 = SSIDHS. {a} Fit a multiple regression equation of the form Hy II: .30 + 31x1 + 132412. to the data of Example 11.3 on page 42D. {ti} Estimate the yield Df the chemical reaction for a temperature Df 225C. \fConsider the vehicle data from Consumer Reports in Figure 11.3 on page 44D. Weight is in to ns, mileage in miles per gallon, and drive raljo is also indicated. A regression model was tted relating weight xto mileage y. A partial 3A3 printout in Figure 11.3(l on page 44o shows some of the results of that regression analysis, and Figure 11.31 on page 441 gives a plot of the residuals and weight for each vehicle. {a} From the analysis and the residual plot, does it appear that an improved model might be found by using a transformation? Explain. {h} Fitthe model by replacing weight 1with log weight. Comment on the results. {c} Fit a model by replacing mpg with gallons per 10D miles traveled, as mileage is often reported in other countries. 1I.I'I.I'hich of the three models is preferable? Explain. In Relief frbm Arthritis published by Thorsons Publishers, Ltd., John E. Crolt claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced bv a particular species of mussel found off the coast of New Zealand. To test this claim, the mussel extract is to be given to a group of i" osteoarthritic patients. If 3 or more ofthe patients receive relief, we shall not reject the null hypothesis that p = [14; otherwise, we conclude that p a: o4. {a} Evaluate o, assuming that p = {14. {b} Evaluate 18 for the alternative p = [13