You have the following partial output from Minitab about a regression model invo

Question

You have the following partial output from Minitab about a regression model involving two predictors. Analysis of Variance Regression Equation Y = 24.97 + 11.9003 X1 - 1.8051 X2 - 3.5437 X3 + 5.4017 X4 a) Complete the ANOVA table. b) What is the 95% confidence interval on the regression confidence for X1 c) With 99% confidence, do you accept that there is a relationship described by hypothesis test on the regression)? d) Estimated R^2 and the Adjusted R^2 e) Can we set the coefficient of X2 to 12 with 95% confidence in doing so?

Explanation / Answer

(a)

(b) The regression coefficient is 11.9003

SE for the regreesion coefficient = sqrt (residual error/n-2) = sqrt(54/23) = 1.532

t-value for 95% confidence interval at df = 24 = 2.064

So, the confidence interval is (11.9003 - 2.064* 1.532, 11.9003 + 2.064* 1.532)

= (8.738, 15.062)

(c) As, the p-values for all the variables is less than the confidence interval 0.01, we reject the null hypothesis and accept that there is relationship described by the model.

(d) R-sq = 160483/160537 = 0.9996

Adj R-sq = 1 - ((1-R-sq)(n-1)/(n-k-1))

n = 25, k = 4

Adj R-sq = 1 - ((1-0.9996)(25-1)/(25-4-1))

= 0.99952

Source DF Adj SS Adj MS F-Value P-value Regression 4 160483 40120.75 14859.54 2.039131e-34 X1 1 87096 87096 32464.4 1.379341e-33 X2 1 27158.6 27158.6 645.22 0 X3 1 14876.3 14876.3 5545.06 6.343234e-26 X4 1 31352.1 31352.1 11686.3 3.736282e-29 Error 20 54 2.7 Total 24 160537 6689.042

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