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

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

(b) Compute the residuals.

(c) Compute SSE and estimate the variance.

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

(e) Show that SST SSR SSE.
(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).

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