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Chapter 14: Q. 14.21 (page 561)

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^=2.875−0.625x

Short Answer

Expert verified

a. The standard error of the estimate is ≈1.88

b. The residual plot is

c. The normal probability plot of the residuals is,

Step by step solution

01

Part (a) Step 1: Given Information

Given table: y^=2.875−0.625x

02

Part (a) Step 2: Explanation

Exercise 1514 MINITAB Output:

Analysis of Variance:

According to the output from the analysis of variance,

We know SSE=10.625,

df=n-2=5-2=3

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

se=SSEn−2=10.6253=3.541666667=1.881931632≈1.88

03

Part (b) Step 3: Given Information

Given table: y^=2.875−0.625x

04

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 xin Predictors.
Step4:InGraphs,underResidualsvsthevariables,inputthecolumnsxvariables.
Step 5: Click the OK button.

The Residual Plot is as follows:

05

Part (c) Step 5: Given Information

Given table: y^=2.875−0.625x

06

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 xcolumns.
Step4:SelectNormalprobabilityplotofresidualsfromtheGraphsmenu.
Step 5: Click the OK button.

The Normal probability plot of the residuals is:

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Most popular questions from this chapter

In this Exercise 14.53, we repeat the information from Exercise 14.17.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

role="math" localid="1652352243033" x22344y34021 y^=5-x

Following are the age and price data for corvettes, use α=0.10

presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(f)
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95%confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence inter. val that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.99 U.S. Presidents. The data from Exercise 14.35 for the ages at inauguration and of death of the presidents of the United States are on the WeissStats site. Specified value of the predictor variable: 53 years.

14.93 Corvette Prices. Following are the age and price data for Corvettes from Exercise 14.23.

x
6
6
6
2
2
5
4
5
1
4
y
290
280
295
425
384
315
355
328
425
325

a. Obtain a point estimate for the mean price of all 4-year-old Corvettes.

b. Determine a 90% confidence interval for the mean price of all 4-year-old Corvettes.

c. Find the predicted price of a 4-year-old Corvette.
d. Determine a 90% prediction interval for the price of a 4 -year-old Corvette.
e. Draw graphs similar to those in Fig. 14.11 on page 576 , showing
f. Why is the prediction interval wider than the confidence interval?

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b) - (h).
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95% confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.103 High and Low Temperature. The data from Exercise 14.31for average high and low temperatures in January of a random sample, of 50cities are on the WeissStats site. Specified value of the predictor variable: 55°F.
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