Operating Capacity and Profits for Twelve Manufacturing Plants X = % of Operatin
ID: 3224007 • Letter: O
Question
Operating Capacity and Profits for Twelve Manufacturing Plants X = % of Operating Capacity y = Profits in Thousands of Dollars Use these data for Questions on this task. Estimate the linear regression coefficients and write out the estimated linear regression equation. Use Statcrunch to find the t-value and associated P-value for the slope of the regression line. H0: beta_1 = 0 versus Ha: beta_1 notequalto 0 with alpha = 0.05 Conduct the above test of hypothesis using the t-value and associated P-value obtained from Statcrunch. Construct a 95% confidence interval for beta_1.Explanation / Answer
Ans
1]
> x=c(51,57,61,65,77,80,82,87,89,91,95,97)
> y=c(3.0,6.2,3.1,4.2,7.3,4.5,6.1,9.7,10.0,14.2,16.1,18.1)
> fit=lm(y~x)
> fit
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
-13.0315 0.2778
> beta0=fit$coefficients[1]
> beta0
(Intercept)
-13.03155
> beta1=fit$coefficients[2]
> beta1
x
0.2777667
Linear regression equation
y= -13.03155 + 0.2777667 x
2]
> summary(fit)
Call:
lm(formula = y ~ x)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -13.03155 4.50436 -2.893 0.016022 *
x 0.27777 0.05696 4.877 0.000645 ***
---
3]
> varcov=vcov(fit)
> seb1=sqrt(varcov[2,2])
> seb1
[1] 0.05695561
> if(abs(beta1/seb1)>qt(0.025,df=length(y)-2))
+ {
+ print("Reject the Null Hypothesis")
+ }else
+ {
+ print("Do not reject the Null Hypothesis")
+ }
[1] "Reject the Null Hypothesis"
4] 95% confidence interval for beta 1
> CI=sort(c(beta1-(qt(0.025,df=length(y)-2)*seb1),beta1+(qt(0.025,df=length(y)-2)*seb1)))
> CI
x x
0.1508617 0.4046717
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