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Chapter 4: Q. 4.103 (page 182)

For Exercises 4.98 - 4.103,

(a) Compute SST, SSR, SSE using formula 4.2 on page 179.

(b) Compute the coefficient of determination, r2.

(c) Determine the percentage of variation in the observed values of the response variable explained by the regression and interpret your answer.

(d) State how useful the regression equation appears to be for making predictions.

Follwing are the study time and score for calculus students from Exercise 4.63.

Short Answer

Expert verified

(a) The values areSST=188;SSR=112.89;SSE=75.11

(b) The coefiicient of variation is 0.60.

(c) The percentage of variation is60%.

(d) The regression line appears to be extremely useful.

Step by step solution

01

Part (a) Step 1. Given Information.

A table of values.

02

Part (a) Step 2. Construct the table.

Construct the table.

03

Part (a) Step 3. Compute SST, SSR, SSE.

Find SST, SSR, SSE.

SST=鈭�yi2-(鈭�yi)2n=54638-(660)28=188

SSR=[鈭�xiyi-(鈭�xi鈭�yin)2鈭�xi2-(鈭�xi)2n=[9519-(117)(660)8]21869-(117)28=112.89

SSE=SST-SSR=188-112.89=75.11

04

Part (b) Step 1. FInd the coefficient of determination. 

r2=SSRSST=112.89188=0.6

05

Part (c) Step 1. Find the percentage of variation. 

Since the coefficient of variation is 0.60,then60% of the variation in the observed value is explained by the regression.

06

Part (d) Step 1. Useful for making predictions. 

The regression line appears to be extremely useful.

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Most popular questions from this chapter

A Knight-Ridder News Service article in an issue of the Wichita Eagle discussed a study on the relationship between country music and suicide. The results of the study. coauthored by S. Stack and J. Gundlach, appeared as the paper "The Effect of Country Music on Suicide" (Social Forces, Vol. 71, Issue 1. Pp. 211-218). According to the article, " analysis of 49 metropolitan areas shows that the greater the airtime devoted to country music. the greater the white suicide rate," (Suicide rates in the black population were found to be uncorrelated with the amount of country music airtime.)

(a). Use the terminology introduced in this section to describe the statement quoted above.

(b). One of the conclusions stated in the journal article was that country music "nurtures a suicidal mood" by dwelling on marital status and alienation from work. Is this conclusion warranted solely on the basis of the positive correlation found between airtime devoted to country music and white suicide rate? Explain your answer.

Acreage and Value. The data from Exercise 4.73 for lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area are on the WeissStats site.

For a data set consisting of two data points:

a. identify the regression line.

b. What is the sum of squared errors for the regression line? Explain your answer.

Study Time and Score. The negative relation between study time and test score found in Exercise 4.63has been discovered by many investigators. Provide a possible explanation for it.

What can you say aboutSSE, SSR and the utility of the regression equation for making predictions if

a. r2=1?

b.r2=0?
See all solutions

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