Consider the electric power consumption data in Exercise 12-10 (a) Calculate R2
ID: 3365541 • Letter: C
Question
Consider the electric power consumption data in Exercise 12-10 (a) Calculate R2 for this model. Interpret this quantity (b) Plot the residuals versus and versus each regressor. Interpret this plot. (c) Construct a normal probability plot of the residuals and comment on the normality assumption. 12-10. The electric power consumed each month by a chemi- cal plant is thought to be related to the average ambient tem perature (x the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in Table E12-2. (a) Fit a multiple linear regression model to these data. (b) Estimate (c) Compute the standard errors of the regression coefficients Are all of the model parameters estimated with the same precision? Why or why not? (d) Predict power consumption for a month in which x,-75F, x2 = 24 days, X,-90%, and X4-98 tons. TABLE- E12-2 Power Consumption Data 24 240 236 270 274 301 316 300 296 267 276 288 261 25 100 95 110 90 45 60 65 72 80 84 75 60 50 38 24 25 25 26 25 25 24 25 25 23 87 94 94 87 86 97 96 110 105 100 98 90 89Explanation / Answer
a) Ans: The multiple linear regression is
The regression equation is
y = - 123 + 0.757 x1 + 7.52 x2 + 2.48 x3 - 0.481 x4
Predictor Coef SE Coef T P
Constant -123.1 157.3 -0.78 0.459
x1 0.7573 0.2791 2.71 0.030
x2 7.519 4.010 1.87 0.103
x3 2.483 1.809 1.37 0.212
x4 -0.4811 0.5552 -0.87 0.415
S = 11.7866 R-Sq = 85.2% R-Sq(adj) = 76.8%
b) Ans: Estimate of Sigma Sq= S^2 = 11.7866^2=138.92
c) Ans:
Predictor Coef SE Coef T P
Constant -123.1 157.3 -0.78 0.459
x1 0.7573 0.2791 2.71 0.030
x2 7.519 4.010 1.87 0.103
x3 2.483 1.809 1.37 0.212
x4 -0.4811 0.5552 -0.87 0.415
The standard error of the coefficient is given to the third column above matrix.
d) Ans: The predicted power consumtion for a month in which x1=75F, x2=24days, x3=90% and 98 tones is
y = - 123 + 0.757 *75 + 7.52 *24+ 2.48 *90 - 0.481 *98=290.317.