An article in the Journal of the Environmental Engineering Division ("Least Squares Estimates of BOD Parameters," Vol. 106, 1980, pp. 1197-1202) describes the results of testing a sample from the Holston River below Kingport, TN, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting date is shown below: Time (days) BOD (mg/liter) 0.6 2 0.7 4 1.5 6 1.9 8 2.1 10 2.6 12 2.9 14 3.7 16 3.5 18 3.7 20 3.8Minitab output resulting from fitting a simple linear regression model with time as the explanatory variable and BOD as the response follows. Predictor Coef SE Coef T P Constant 0.6578 0.1657 3.97 0.003 Time 0.17806 0.01400 12.72 0.000 5 = 0.287281 R-5q = 94.7% R-Sq(adj) = 94.19% Analysis of Variance Source DF 55 MS F P Regression 1 13.344 13.344 161.69 0.000 Residual 9 0.743 0.083 Error Total 10 14.087(a) Assuming that a simple linear regression model is appropriate, estimate the regression model relating BOD (y) to the time (x). Round your final answers to 4 decimal places. i X What is the estimate of a?? Round your final answer to 3 decimal places. i (b) What is the estimate of expected BOD level when the time is 3 days? Round your final answer to 3 decimal places. (c) What change in mean BOD is expected when the time increases by 5 days? Round your final answer to 4 decimal places. (d) Suppose the time used is 2 days. Calculate the fitted value of y and the corresponding residual. Round your final answers to 4 decimal places. D = i i(e) The following is a graph of ) versus the corresponding observed values Vi. Scatterplot of fitted vs BOD 45 35 filled 25 2.0 1.5 1.0. 1.0 1.5 20 2.5 3.0 3.5 40 BOD Which of the following describes what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line? O the points would fall on a horizontal line O the points would fall along a 450 line O the points would be in a completely random pattern O the points would all be equal (f) Does the plot actually obtained indicate that time is an effective regressor variable in predicting BOD? No Yes