A study was conducted on automobile engines to examine the relationship between engine speed measured in revolutions per minute (RPM) and engine torque with the goal of predicting engine torque.

a. Fit a quadratic regression model and state the quadratic regression equation. (Round the X1i coefficient to four decimal places as needed. Round the X1i2 coefficient to six decimal places as needed. Round all other values to one decimal place as needed.)

b. Predict the mean torque for an RPM of 5,000. (Round to two decimal places as needed.)

c. Analyze the residual plots and determine whether the regression model is valid.

d. At the 0.05 level of significance, is there a significant quadratic relationship between torque and RPM? Determine the p-value. (Round to three decimal places as needed.)

e. State the conclusion of the test. Using the following keywords {less than, higher than, reject, do not reject, accept, is, is not}, fill in the blanks and complete the below argument in the most correct way. You don’t need to use all the keywords.

“Since the p-value is ________, the level of significance, _________ H0. There _______a significant quadratic relationship between torque and RPM.

1 2 3 4 5 5 7 3 9 0 1 2 3 4 5 6 7 8. 9 0 1 2 3 4 5 6 7 8. 9 ON 00 oc -0 -1 2 3 4 5 6 -7 8 9 -0 A RPM 1500 1500 B Torque 93,87 103 96,86 90,87 98,53 102,58 102,64 102,81 104 1500 1500 1500 2000 2000 2000 2000 2000 100,8 2500 113,5 2500 112,7 2500 115,15 2500 113,73 2500 110,53 2660 111,65 2660 112,65 2660 111,05 2660 112,54 2660 117,71 2800 117,65 2800 113,18 2800 110,18 2800 113,49 2800 115,95 2940 116,38 2940 114,28 2940 108,57 2940 115,01 2940 3500 3500 107,05 3500 112,58 3500 106,27 3500 107,28 4000 107,76 4000 107,87 4000 106,11 119,2 108,2 C D E PRM F Torque 106,91 111,62 103,16 102,28 107,27 103,91 104,2 100,84 95,17 99,16 96,94 96,75 96,48 95,22 96,8 95,72 97,47 91,29 91,71 87,92 90,32 4000 4000 4500 4500 4500 4500 4500 5000 5000 5000 5000 5000 5225 5225 5225 5225 5225 5500 5500 5500 5500 5500 89,81 5775 77,81 5775 79,95 5775 82,04 5775 81,07 5775 83,16 6000 76,79 6000 74,44 6000 76,7 6000 73,39 6000 74,06 S