Q 5. A Canadian Manufacturing Company owns a complex of nine buildings. For pre-
ID: 3257826 • Letter: Q
Question
Q 5. A Canadian Manufacturing Company owns a complex of nine buildings. For pre- dicting the fuel consumption in heating these buildings, it was suggested to use a linear model with two predictors, temperature and chill index (X2). The following data for 8 week's fuel consumption (Y), average hourly temperature(Xi( F)) and chill index (X2) has been collected. Week Average hourly Chill Fuel i Temperature Index Consumption XI in F) (Y, in tons 28.0 18 12.4 11.7 28.0 14 12.4 32.5 24 10.8 39.0 22 45.9 9.4 57.8 16 9.5 8.0 58.1 62.5 7.5 Partial MINITAB output obtained is given below: Regression Analysis: Y versus X1: The regression equation is Y 15.8 0.128 xi Predictor Coef SE Coef Constant 15.8379 0.8018 19.75 0.000 X1 -0.12792 0.0175 7.333 0.000 Analysis of Variance DF Source SS MS Regression 1 22.981 22.981 53.69 0.000 Residual Error 6 2.568 0.428 Total 7 25.549Explanation / Answer
Answer to part a)
The single most important predictor is "hourly temperature"
this is because the P value of the liear model of Y on x is 0.000 , which is very small indicating significant relation between chill index and fuel consumption
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Answer to part b)
The extra sum of squares added to the regression is SS(x1,x2) model - SS(x2) model
=24.875 - 19.366 = 5.509
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Answer to part c)
Formula used:
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For model Y on x1
R square = 22.981 / 25.549 = 0.8995
R = 0.9484
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For model y on x2
R square = 19.366 / 25.549 = 0.758
R = 0.8706
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For model y on x1 and x2
R square = 24.875 / 25.549 = 0.9736
R = 0.9867
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Thus we find that the model with x1 and x2 has the highest value of R, thus it has the best fit and it must be used.
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Answer to part d)
90% confidence interval for x1 will be:
x1 slope - t * SE of x1 , x1 slope + t*SE of x1
[Value of t is based on 90% confidence interval and df = n-(k+1) = (8-(2+1)) = 5]
-0.09 - 2.015 *0.0141 , -0.09 + 2.015 *0.0141
-0.1184 , -0.0616
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90% confidence interval for x2
x2 slope - t * SE of x2, x2 slope + t* SE
0.0825 - 2.015 * 0.022 , 0.0825 + 2.015 *0.022
0.03817 , 0.1268
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