PLEASE DO IN R-STUDIO OTHERWISE PLEASE DON\'T ANSWER. Consider the electric powe

Question

PLEASE DO IN R-STUDIO OTHERWISE PLEASE DON'T ANSWER.

Consider the electric power data in Exercise 12-10. Build regression models for the data using the following techniques (a) All possible regressions. Find the minimum Cp and minimum MSE equations (b) Stepwise regression. (C) Forward selection (d) Backward elimination (e) Comment on the models obtained. Which model would you prefer? 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 2 (c) Compute the standard errors of the regression coefficients Are all of the model parameters estimated with the same precision? Why or why not? x2 24 days, X3-90%, and X4-98 tons. TABLE- E12-2 Power Consumption Data (d) Predict power consumption for a month in which x,-75F, 240 236 270 274 301 316 300 296 267 276 288 261 25 24 100 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 89

Explanation / Answer

fit <- lm(y ~ x1 + x2 + x3 + x4, data = power)

(c) # Forward Selection based on AIC

library(MASS)

step <- stepAIC(fit, direction="forward")

summary(step)

(d) # Backward elimination based on AIC

library(MASS)

step <- stepAIC(fit, direction="backward")

summary(step)

(e) AIC is measure of goodness of fit. It penalize complex models. In other words, it penalize the higher number of estimated parameters. It believes in a concept that a model with fewer parameters is to be preferred to one with more.

The model with the lower AIC score is better.

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