Question: 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.

1. Fit a multiple linear regression model to the data.
2. Predict power consumption for a month in which x1 = 75, x2 = 24, x3 = 90, x4 = 98.
3. Test for significance of regression using a = 0.05. What is the P-value of this test?
4. Estimate \({{\sigma }^{2}}\).
5. Use the t-test to assess the contribution of each regressor to the model. Using a = 0.05, what conclusions can you draw?
6. Find 95% confidence intervals on 01, 02, 03, 04.
7. Find a 95% confidence interval on the mean of Y for the values of regressors from b).
8. Find a 95% prediction interval on the power consumption for the values of regressors from b).
9. Calculate R2 and adjusted R2 for this model. Interpret these quantities.
10. Plot the residuals versus ˆy. Interpret this plot.
11. Construct a normal probability plot of the residuals and comment on the normality assumption.

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