The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table:

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and th tons of product produced (x4). The past year's historical data are available and are presented in the following table: y X1 3 T4 240 25 24 91 100 236 31 21 90 95 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 3 23 89 98 (a) Fit a multiple linear regression model to these data. Estimate regression coefficients and o. (b) What are the standard errors of the regression coefficients. (c) Test for significance of regression using a = 0.05. What is the P-value for this test? (d) Use the t-test to assess the contribution of each regressor to the model. Using a = 0.05, what conclusions can you draw? (e) Find 99% confidence intervals on B1, B2, B3 and B4. (f) Predict power consumption for a month in which x1 = 75F, x2 = 24 days, X3 = 90%, and x4 = 98 tons. Find a 90% confidence interval on the mean of Y in this case. g) Find a 90% prediction interval on the power consumption for the case in part (f). (h) Calculate R- for this model. Interpret this quantity. i) Plot the residuals versus the fitted values. Interpret this plot. () Construct a normal probability plot of the residuals, and perform Shapiro test on them. Then, comment on the normality assumption