(a) Examine the calibration plot and the plot of the residualse on the fitted values Ý for the multiple regression of th
Posted: Wed May 11, 2022 7:56 pm
- A Examine The Calibration Plot And The Plot Of The Residualse On The Fitted Values Y For The Multiple Regression Of Th 1 (54.63 KiB) Viewed 22 times
- A Examine The Calibration Plot And The Plot Of The Residualse On The Fitted Values Y For The Multiple Regression Of Th 2 (14.4 KiB) Viewed 22 times
(b) Revise the variables in the model so all are on the scale defined by log 10. Has this transformation fixed the problems identified in part (a)? To answer this question, refit the model on the log scale and consider the calibration and residual plots for the revised model. Note that an equation of the form bo b. by log 10V = bo + by log 10x7 + b2log 10x3 is equivalent to the product y = 10°oxy! x?? The slopes in the log-log regression are exponents in a model that estimates y as the product of the explanatory variables raised to different powers. These powers are the partial elasticities of the response with respect to the predictors. Construct the calibration plot. Choose the correct graph below. ОА. OB. OC. OD HE Comb. log MPG) HHHHH H > → HHH Est. Comb.log(MPG) Est. Comb. log(MPG) Est. Comb.log(MPG) Est. Comb. log(MPG) . Plot the residuals on log 10 (î). Choose the correct graph below. OA. OB OC. OD A Residual 0.2- A Residual 0.21 A Residual 0.24 A Residual 0.2 Q Q .. HHH > -0.22 Est. Comb.log(MPG) -0.2 Est. Comb.log(MPG) -0.22 Est. Comb. log(MPG) -0.2 Est. Comb.log(MPG) Has this transformation fixed the problems identified in part (a)? Select all that apply. A. There is no longer a nonlinear pattern in the residual plot. This problem has been fixed. B. The calibration plot no longer suggests R is very low. This problem has been fixed. C. There is no longer a linear pattern in the residual plot. This problem has been fixed. D. There is still a linear pattern in the residual plot. This problem has not been fixed. E. The calibration plot still suggests R’ is very low. This problem has not been fixed. OF. There is still a nonlinear pattern in the residual plot. This problem has not been fixed. O G. No problems were identified in part (a).
(c) Is the partial elasticity for weight equal to zero? Estimate the partial elasticity from the multiple regression of log 10 MPG on log 10HP and log 10 weight. What are the null and alternative hypotheses? O A. Ho: Pweight *0 Hai Bweight = 0 OC. Ho: Pweight = 0 Ha: Bweight 70 OB. Ho: Pweight = 0 Ha: Pweight > 0 OD. Ho: Pweight = 0 Ha: Pweight <0 What is the test statistic? tweight =(Round to two decimal places as needed.) What is the p-value? p-value = (Round to three decimal places as needed.) What is the proper conclusion at a = 0.05? H. The partial elasticity for weight V significantly zero (d) Compare the partial elasticity for weight (the slope for log 10 weight in the multiple regression) to the marginal elasticity for MPG with respect to weight (the slope for log 10 weight in a simple regression of log 10 MPG on log 10 weight). Are these estimates very different? Use confidence intervals to measure the size of any differences The 95% confidence interval for the partial elasticity for weight is to 11 (Round to three decimal places as needed.) The 95% confidence interval for the marginal elasticity for weight is to | (Round to three decimal places as needed.) Are these estimates very different? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Yes. The confidence intervals suggest the value of the partial elasticity is less than the marginal elasticity by about (Round to the nearest whole number as needed.) OB. Yes. The confidence intervals suggest the value of the partial elasticity is greater than the marginal elasticity by about (Round to the nearest whole number as needed.) O C. No. The estimates are not very different.
(e) Does the path diagram for this model offer an explanation for the differences in the confidence intervals found in part (d)? Explain. Choose the correct answer below. O A. Yes, because adding the direct effect from the weight to the indirect effect from the weight results in a value less than the direct weight. O B. Yes, because adding the direct effect from the weight to the indirect effect from the weight results in a value greater than the direct weight. OC. No, because adding the direct effect from the weight to the indirect effect from the weight results in a value less than the direct weight. OD. No, because adding the direct effect from the weight to the indirect effect from the weight results in a value greater than the direct weight. O E. The part (d) estimates are not very different. (f) Based on this analysis, describe the effect of weight on MPG. Does it have an effect? Do heavier cars get worse mileage on average? because the 95% confidence interval for the partial elasticity for weight contains only negative values No, zero only positive values Yes, the 95% confidence interval for the marginal elasticity
3625 4000 Combined_MPG Weight_(pounds) 24 25 4000 25 3875 28 4000 18 6000 16 4250 14 4250 14 4000 21 4250 17 4250 21 3875 26 3625 13 4500 15 4500 13 4500 14 4500 15 4750 16 16 4000 15 4000 15 4500 13 6000 22 3500 21 3625 22 4000 231 3625 17 4500 17 4750 17 4500 20 4750 17 5000 16 4500 30 3000 30 3000 30 3250 30 3125 30 3125 28 3500 29 3375 30 3000 32 2875 19 5250 14 5500 19 5000 14 5500 24 3750 21 4500 18 4750 30 2750 33 2750 Horsepower 200 211 211 211 225 430 430 525 333 354 200 265 470 470 510 510 470 430 420 419 490 505 230 230 300 300 400 400 400 316 400 414 122 122 122 180 180 180 180 180 122 300 555 300 555 173 292 359 100 100