The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four predictor variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (Load in tons), (3) average driving speed (Speed in mph ), and (4) oil change interval (Oil in 1,000s of miles). The accompanying data file shows the results for 25 trucks. Click here for the Excel Data File b. Predict the time before the first engine overhaul for a particular truck driven 65,000 miles per year with an average load of 19 tons, an average driving speed of 53mph, and 16,000 miles between oil changes. Note: Do not round intermediate calculations. Round final answer to 3 decimal places. c. Calculate and interpret the 90% confidence interval for the mean time before the first engine overhaul given the values for the predictor variables from part b. Note: Round final answers to 2 decimal places. d. Calculate and interpret the 90% prediction interval for the time before the first engine overhaul given the values for the predictor variables from part b. Note: Round final answers to 2 decimal places. \begin{tabular}{|c|c|c|c|c|c|} \hline & A & B & C & D & E \\ \hline 1 & Time & Miles & Load & Speed & Oil \\ \hline 2 & 8 & 42.8 & 20 & 47 & 17 \\ \hline 3 & 0.7 & 98.7 & 23 & 49 & 25 \\ \hline 4 & 8.2 & 43.8 & 25 & 67 & 17 \\ \hline 5 & 1.1 & 110.3 & 27 & 64 & 31 \\ \hline 6 & 1.3 & 101.9 & 27 & 49 & 16 \\ \hline 7 & 2.2 & 97.3 & 21 & 67 & 17 \\ \hline 8 & 2.1 & 92.8 & 26 & 51 & 19 \\ \hline 9 & 7.7 & 54.1 & 23 & 70 & 16 \\ \hline 10 & 8.3 & 51.8 & 21 & 54 & 21 \\ \hline 11 & 4 & 85.3 & 26 & 60 & 24 \\ \hline 12 & 0.3 & 120.4 & 31 & 49 & 20 \\ \hline 13 & 5 & 77.9 & 30 & 51 & 29 \\ \hline 14 & 5.2 & 69 & 16 & 50 & 26 \\ \hline 15 & 5.5 & 54.9 & 22 & 62 & 21 \\ \hline 16 & 5.3 & 66.3 & 25 & 54 & 21 \\ \hline 17 & 8.6 & 39.6 & 17 & 48 & 19 \\ \hline 18 & 5.6 & 52.5 & 24 & 60 & 22 \\ \hline 19 & 5.6 & 54.7 & 24 & 45 & 21 \\ \hline 20 & 4.5 & 74.5 & 17 & 68 & 27 \\ \hline 21 & 6.1 & 58.6 & 21 & 56 & 12 \\ \hline 22 & 6.8 & 52 & 17 & 58 & 24 \\ \hline 23 & 6.9 & 68.4 & 13 & 46 & 24 \\ \hline 24 & 4 & 94.6 & 24 & 54 & 22 \\ \hline 25 & 7.5 & 46.1 & 14 & 62 & 15 \\ \hline 26 & 6 & 61.3 & 22 & 60 & 15 \\ \hline \end{tabular} 27 28 29