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




(a) Assuming that a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). What is the estimate of σ 2?
(b) What is the estimate of expected steam usage when the average temperature is 55 oF?
(c) What change in mean steam usage is expected when the monthly average temperature changes by 1oF?
(d) Suppose the monthly average temperature is 47oF. Calculate the fitted value of y and the corresponding residual.

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