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.

$y=1.75+0.25x$

Short answer

a. The standard error of the estimate is $\approx 1.41$

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: $y=1.75+0.25x$

Part (a) Step 2: Explanation

Exercise 1514 MINITAB Output:

Analysis of Variance:

According to the output from the analysis of variance,

We know SSE $SSE=4$

$$\begin{gathered} df=n-2 \\ =4-2 \\ =2 \end{gathered}$$

The standard error of the estimate is calculated using the formula,

$\begin{array}{rl}& s_e=\sqrt{\frac{SSE}{n-2}}\\ & =\sqrt{\frac{4}{2}}=\sqrt{2}\\ & =1.414213562\\ & \approx 1.41\end{array}$

Part (b) Step 3: Given Information

Given table:$y=1.75+0.25x$

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:

The Residual Plot is as follows:

Part (c) Step 5: Given Information

Given table: $y=1.75+0.25x$

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.

The Normal probability plot of the residuals is: