2. The electric power consumed each month by a chemical plant is thought to be r

Question

2. The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (r), the umber of days in the month (z2), the average product purity (zs), and the tons of product produced () 240 25 24 91 100 236 31 21 90 95 270 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 23 89 9 Call: a(formula xix2 x3 + x4) Residuals: Min 1Q Median 3Q Max -14.098 -9.778 1.767 6.798 13.016 Coefficients: Estinate Std. Error t value Pr>lt) (Intercept) -123.1312 157.2561 -0.783 0.459 X1 X2 X3 X4 0.7573 0.2791 2.713 0.030 7.5188 4.0101 1.875 0.103 1.8094 1.372 0.212 -0.4811 0.5552 -0.867 0.415 2.4831 Signif. codes: 00.0010.01 0.05 . 0.1 1 Residual standard error: 11.79 on 7 degrees of freedon Multiple R-squared: 0.852, Adjusted R-squared: 0.7675 F-statistic: 10.08 on 4 and 7 DF, p-value: 0.00496 (a) Write down the fitted least squares regression model. (b) What is the value of the estimate of (c) Find the value of R2 and how to interpret it? (d) Test the hypothesis at = 0.05: Ha : at least one of them is nonzero.

Explanation / Answer

a, Y= 0.7573*X1+7.5188*X2+2.4831*X3-0.4811*X4-123.1312

b, The value of estimated sigma is

=std error * sqrt(n)

=31.193

c, R squared value is 0.852 which means that the model fitted is quite good.

d, At 5% LOS we rejet the null hypothesis since X2 seems to be insignificant at 5% LOS.

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