Find a $95\%$prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

Using MINITAB, calculate the point estimate for the conditional mean of the response variable that corresponds to the predictor variable, $x=2$.

Procedure for MINITAB:

Step 1: Select Regression > Regression from the Stat menu.

Step 2: In the Response box, type $y$.

Step 3: In Predictors, fill in the $x$ columns.

Step 4: Under Prediction interval for fresh observations, put $2$ in Options.

Step 5: Type $95$ in the Confidence Level box.

Step 6: Select Fits, Confidence Limits, SEs of Fits, and Prediction Limits in Storage.

Step 7: Click the OK button.

MINITAB Output:

• MINITAB is used to calculate the $95\%$confidence interval for the conditional mean of the response variable corresponding to the predictor variable $x=2$.
• The $95\%$confidence interval for the conditional mean of the response variable corresponding to the predictor variable $x=2$is $(-5.8868,21.8868)$, according to the MINITAB output in part (a).

• MINITAB is used to calculate the predicted value of the response variable corresponding to the predictor variable$x=2$.
• The anticipated value of the response variable corresponding to the predictor value $x=2$ is $8$ according to the MINITAB output in part (a).

• MINITAB is used to calculate the $95\%$prediction interval for the conditional mean of the response variable corresponding to the predictor variable $x=2$.
• The $95\%$predictioninterval for the conditional mean of the response variable corresponding to the predictor variable $x=2$is $(-17.6059,33.6059)$, according to the MINITAB output in part (a).