4 The number of pounds of steam used per month by a chemical

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.

Solution

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