Consider the data and simple linear regression model in Exercise 6-2.

(a) Find the mean pounds of steam given that the ambient temperature is 52 degrees.

(b) Compute a 99% CI on this mean response.

(c) Compute a 99% PI on a future observation when the ambient temperature is equal to 52 degrees.

(d) What do you notice about the relative size of these two intervals? Which is wider and why?

Exercise 6-2

For Exercises 6-1 through 6-5, perform the following.

(a) Estimate the intercept ?₀ and slope ?₁ regression coefficients. Write the estimated regression line.

(b) Compute the residuals.

(c) Compute SS_E?and estimate the variance.

(d) Find the standard error of the slope and intercept coefficients.

(e) Show that SS_T?= SS_R?+ SS_E.

(f) Compute the coefficient of determination, R². Comment on the value.

(g) Use a t-test to test for significance of the intercept and slope coefficients at ? = 0.05. Give the P-values of each and comment on your results.

(h) Construct the ANOVA table and test for significance of regression using the P-value. Comment on your results and their relationship to your results in part (g).

(i) Construct 95% CIs on the intercept and slope. Comment on the relationship of these CIs and your findings in parts

(g) and (h).

(j) Perform model adequacy checks. Do you believe the model provides an adequate fit?

(k) Compute the sample correlation coefficient and test for its significance at ? = 0.05. Give the P-value and comment on your results and their relationship to your results in parts (g) and (h).

The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in ⁰F) for that month. The past year?s usage and temperature are shown in the following table.

Step-by-ste

Usage/ 1000 y 21 185.79 24 214.47 32 288.03 424.84 50 454.58 59 539.03 Temp. x Month Jan. Feb. Mar. Apr. 47 May June Month July Aug. Sept. Oct. Nov. Dec. Temp. X 68 74 62 50 41 30 Usage/ 1000 y 621.55 675.06 562.03 452.93 369.95 273.98