Question

II) (10 marks) 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. An investigator has collected the past year's usage and temperature in a table. Some summary statistics related to this dataset are provided y-5062.212x,2-29256, n 12 , x,-558, y,2 2416144 Xiy.-265864.6, (yi-%)2-37.746 Month Temp. Usage/1000 Jan 21 Feb 24 Mar. 32 Apr. 47 May 50 June 59 July 68 Aug. 74 Sept. 62 Oct. 50 Nov. 41 Dec 30 185.79 214.47 288.03 424.84 454.58 539.03 621.55 675.06 562.03 452.93 369.95 273.98 a) Assume that a simple linear regression model is appropriate. Fit the regression model relating steam usage (y) to the average temperature (X) and estimate parameters βοΆ,02 b) Does it appear that there is a useful linear relationship between these two variables? Answer c) The investigator wishes to have a 95% confidence interval forA, calculate and interpret the d) What proportion of total variability is accounted for by this simple linear regression model? Interpret the estimated parameters the question by employing the critical value approach when a required confidence interval. 0.01. Comment on the strength and the direction of the correlation between temperature and steam usage Calculate a 95% prediction interval for steam usage when the temperature is 70°F e)

Answer 1

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