1.) Find the data for problem 6-17 in the pdf file posted to Ch. 6 slides named

Question

1.) Find the data for problem 6-17 in the pdf file posted to Ch. 6 slides named Ch6HWProblems.pdf. Use Excel to develop a multiple regression model and use hypothesis testing to determine whic of the model constants (B0, B1, etc.) are significant. In your final model, what should the value of B0_hat be?

2.) In your final model, what should the value of B1_hat be?

3.) In your final model, what should the value of B2_hat be?

4.) In your final model, what should the value of B3_hat be?

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (xi), the number of days in the month (xa), the average product purity (xs), and the tons of product produced (x.). The past year's historical data are available and are presented in the 240 25 236 31 270 45 274 301 316 72 26 300 25 24 21 24 25 65 25 9 91 90 100 95 110 60 94 94 87 86 97 267 75 24 88 10 25 276 288 50 25 90 26 38 23 89 105 100 98 60 91

Explanation / Answer

> model<-lm(Y~.,data=df)
> summary(model)

Call:
lm(formula = Y ~ ., data = df)

Residuals:
Min 1Q Median 3Q Max
-25.933 -7.407 4.551 8.531 19.228

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 182.1637 221.4246 0.823 0.43781
X1 1.0442 0.2944 3.546 0.00939 **
X2 -1.1718 2.2428 -0.522 0.61746
X3 0.8622 1.6831 0.512 0.62422
X4 -0.1390 0.8425 -0.165 0.87360
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 17.42 on 7 degrees of freedom
Multiple R-squared: 0.6767, Adjusted R-squared: 0.4919
F-statistic: 3.662 on 4 and 7 DF, p-value: 0.06474

> mse <- function(sm)
+ mean(sm$residuals^2)
> mse(model)
[1] 177.1026
> new <- data.frame(t(c(75,24,90,98)))
> names(new)<-c("X1","X2","X3","X4")
> predict(model, new, se.fit = TRUE)
$fit
1
296.3258

$se.fit
[1] 9.365147

$df
[1] 7

$residual.scale
[1] 17.42425

Model:

Coefficients:
(Intercept) X1 X2 X3 X4
182.1637 1.0442 -1.1718 0.8622 -0.1390

Y=182.1637 +1.0442X1-1.1718X2+0.8622X3-0.1390X4

predicted value: 296.3258

estimated sigma square : 177.1026

X3 and X4 are significant

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