91Ó°ÊÓ

Given,

\(x=3\)

Find the point estimate for the conditional mean of the response variable corresponding to the predictor variable, \(x=2\) by using MINITAB. MINITAB procedure:

Step 1: Choose Stat > Regression > Regression.

Step 2: In Response, enter the column y.

Step 3: In Predictors, enter the columns X.

Step 4: In Options, enter \(3\) under Prediction interval for new observations

Step 5: In Confidence Level, enter \(95\).

Step 6: In Storage, Choose Fits, Confidence limits, SEs of fits, and Prediction limits.

Step 7: Click OK

MINITAB output: Predicted Values for New Observations

From the MINITAB output, the point estimate for the conditional mean of the response variable corresponding to the predictor variable \(x=3\) is \(2\).

From the MINITAB output in part (a), the confidence interval for the conditional mean of the response variable corresponding to the predictor variable \(x=3\) is \((-0.013, 4.013)\).

Hence, the confidence interval for the conditional mean is \((-0.013, 4.013)\).

From the MINITAB output in part (a), the predicted value of the response variable corresponding to the predictor variable \(x=3\) is \(2\)

Hence, the predicted value of the response variable corresponding to the predictor variable \(x=3\) is \(2\).

From the MINITAB output in part (a), the prediction interval for the conditional mean of the response variable corresponding to the predictor variable \(x=3\) is \((-2.930, 6.930)\)

Hence, \(95%\) prediction interval for the conditional mean is \((-2.930, 6.930)\)