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Chapter 14: Q. 14.19 (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^=1+2x

Short Answer

Expert verified

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

01

Part (a) Step 1: Given Information

Given table:y^=1+2x

02

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(Y)variable.
Step 3: Fill in the columns containing the predictor (X)variables in Predictors.
Step 4: Click the OK button.

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

03

Part (b) Step 3: Given Information

Given table:

y^=1+2x

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.
Step5:ClicktheOKbutton.

MINITAB output:

05

Part (c) Step 5: Given Information

Given table: y^=1+2x

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.

MINITAB output:

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Most popular questions from this chapter

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

The figure shows three residual plots and a normal probability plot of residuals. For each part, decide whether the graph suggests a violation of one or more of the assumptions for regression inferences. Explain your answers.

For two variables satisfying Assumptions 1-3 for regression inferences, the population regression equation is y=20-3.5x. For samples of size 10 and given values of the predictor variable, the distribution of slopes of all possible sample regression lines is a --------distribution with mean------- .

Gas Guzzelrs. Use the data on the WeissStats site for gas mileage and engine displacement for 121vehicles referred to in Exercise 14.41

a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).

b. Decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

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?
See all solutions

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