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Chapter 4: Q. 4.100 (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.

Following are the size and price data for the custom homes from Exercise 4.60.

Short Answer

Expert verified

(a) The values areSST=79444.89;SST=54562.45;SSE=24882.44

(b) The coefiicient of variation is r2=0.687.

(c) The percentage of variation is68.7%.

(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=3504412-(5552)29=79444.89

SSR=[鈭�xiyi-(鈭�xi鈭�yin)2鈭�xi2-(鈭�xi)2n=[169993-(270)(5552)9]28316-(270)29=54562.45

SSE=SST-SSR=79444.89-54562.45=24882.44

04

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

r2=SSRSST=54562.4579444.89=0.687

05

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

Since the coefficient of variation is 0.687,then 68.7% 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

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.

Birdies and Score. The data from Exercise 4.70 for number of birdies during a tournament and final score for 63women golfers are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

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Fill in the blanks.

a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.

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