Please answer exercise 11.2.9 and 11.4.9 stepwise showing all necessary steps

a. Calculate the least square estimates of the slope and inter- cept. What is the estimate of o7? Graph the regression model and the data. b. Find the estimate of the mean deflection if the stress level can be limited to 65%. c. Estimate the change in the mean deflection associated with a 5% increment in stress level. d. To decrease the mean deflection by one millimeter, how much increase in stress level must be generated? e. Given that the stress level is 68%, find the fitted value of deflection and the corresponding residual. 11.2.9 cD An article in the Journal of the Environmental Engineering Division [\"Least Squares Estimates of BOD Param- eters\" (1980, Vol. 106, pp. 1197-1202)] took a sample from the Holston River below Kingport, Tennessee, during August 1977. The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days): 1 2 4 6 && 10 12 14 #16 18 20 0.6 0.7) 1.5 2.6 2.9 3.7 3.5 3.7 3.8 BOD (mg/liter): 19 2.1 a. Assuming that a simple linear regression model is appro- priate, fit the regression model relating BOD (y) to the ime (x). What is the estimate of o7? b. What is the estimate of expected BOD level when the time is 15 days? c. What change in mean BOD is expected when the time changes by 3 days? d. Suppose that the time used is 6 days. Calculate the fitted value of y and the corresponding residual. e. Calculate the fitted }, for each value of x, used to fit the model. Then construct a graph of , versus the corresponding observed values y; and comment on what this plot would look like if the relationship between y and x was a deterministic (no random error) straight line. Does the plot actually obtained indicate that time is an effective regressor variable in pre- dicting BOD? 11.2.10 Show that in a simple linear regression model the point (x, ) lies exactly on the least squares regression line. 11.4.9 cD Consider the data in Exercise 11.2.9 on y = oxygen demand and x = time. a. Test for significance of regression using o = 0.01. Find the P-value for this test. What conclusions can you draw? b. Estimate the standard errors of the slope and intercept. c. Test the hypothesis that B, = 0