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:

(a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables and the dependent variable.

(b) Compute the residuals.

(c) Compute SSE and estimate the variance.

(d) Compute the coefficient of determination, R2, and adjusted coefficient of multiple determination, R2 Adjusted.
Comment on their values.

(e) Construct the ANOVA table and test for significance of regression.
Comment on your results.

(f) Find the standard error of the individual coefficients.
(g) Use a t-test to test for significance of the individual coefficients at 0.05. Comment on your results.
(h) Construct 95% CIs on the individual coefficients.
Compare your results with those found in part (g) and comment.
(i) Perform a model adequacy check, including computing studentized residuals and Cook’s distance measure for each of the observations. Comment on your results.
( j) Compute the variance inflation factors and comment on the presence of multicollinearity.

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y x1 x2 X3 x4 240 25 24 91 100 236 31 21 90 95 290 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 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 23 89 98