4) The number of pounds of steam used per month by a chemical plant is thought t

Question

4) 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 temperatures are in the following table: a) Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). b) What is the estimate of expected stem usage when the average temperature is 55 F? c) Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. d) Calculate the R^2 of the model. e) Find a 95% prediction Interval on stem usage when temperature is 55 F.

Explanation / Answer

b) Plug in x =55

y = 500.104

c) When x=47, predicted y as per regression equation = 426.44

Actual observed is 424.84

Residual = -1.60

d)

r=0.9999

r^2 = 0.9998

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Find XY and X2 as it was done in the table below. X Y XY XX 21 185.79 3901.59 441 24 214.47 5147.28 576 32 288.03 9216.96 1024 47 424.84 19967.48 2209 50 454.58 22729 2500 59 539.03 31802.77 3481 68 621.55 42265.4 4624 74 675.06 49954.44 5476 62 562.03 34845.86 3844 50 452.93 22646.5 2500 41 369.95 15167.95 1681 30 273.98 8219.4 900 Sum 558 5062.24 265864.4 29256 Intercept -6.336 Slope 9.208 Equation is y = 9.208x-6.336

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