Question

In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

$\hat{y}=1+2x$

Short answer

a. The standard error of the estimate is $2.449$

b. The residual plot is

c. The normal probability plot of the residuals is,

Step-by-step solution

Part (a) Step 1: Given Information

Given table:$\hat{y}=1+2x$

Part (a) Step 2: Explanation

MINITAB can be used to calculate the estimate's standard error.

ProcedureforMINITAB:

Step1:SelectStat>Regression>Regressionfromthedrop-downmenu.

Step 2: In the Response column, enter the response$\left(Y\right)$variable.

Step 3: Fill in the columns containing the predictor $\left(X\right)$variables in Predictors.

Step 4: Click the OK button.

The standard error of the estimate is $2.449$based on the MINITAB result.

Part (b) Step 3: Given Information

Given table:

$\hat{y}=1+2x$

Part (b) Step 4: Explanation

MINITAB is used to create the residual plot.

ProcedureforMINITAB:

Step1:SelectStat>Regression>Regressionfromthedrop-downmenu.

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

Step 3: Fill in the columns $x$in Predictors.

Step4:InGraphs,underResidualsvsthevariables,inputthecolumnsxvariables.

Step5:ClicktheOKbutton.

MINITAB output:

Part (c) Step 5: Given Information

Given table: $\hat{y}=1+2x$

Part (c) Step 6: Explanation 

MINITAB is used to create a normal probability plot of residuals.

ProcedureforMINITAB:

Step1:SelectStat>Regression>Regressionfromthedrop-downmenu.

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

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

Step4:SelectNormalprobabilityplotofresidualsfromtheGraphsmenu.

Step 5: Click the OK button.

MINITAB output: