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the coefficient of determination

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Wishwell Tile Company uses the number of construction permits issued to help estimate demand (sales). The firm collected the following data on annual sales and number of construction permits issued in its market area:

No. of Construction Sales

Year Permits Issued (000) (1,000,000)

19X1 6.50 10.30

19X2 6.20 10.10

19X3 6.60 10.50

19X4 7.30 10.80

19X5 7.80 11.20

19X6 8.20 11.40

19X7 8.30 11.30

(a) Which variable is the dependent variable and which is the independent variable?

(b) Determine the estimated regression line.

(c) Test the hypothesis (at the .05 significance level) that there is no relationship between the variables.

(d) Calculate the coefficient of determination. Give an economic interpretation to the value obtained.

(e) Perform an analysis of variance on the regression including an F-test (at the .05 significance level) of the overall significance of the results.

(f) Suppose that 8,000 construction permits are expected to be issued in 19X8. What would be the point estimate of Phoenix Lumber Company's sales for 19X8?

(NOTE: This problem requires the use of statistical tables.)

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Solution Summary

The coefficient of determination is clarified in this solution.

\$2.19

Regression Equation: Slope Coefficient Determination

A sample of 12 homes sold last week in St Paul, Minnesota, is selected. The results are shown below

Home Size (1000 square feet) Home Price (\$1000)
1.4 100
1.3 110
1.2 105
1.1 120
1.4 80
1 105
1.3 110
0.8 85
1.2 105
0.9 75
1.1 70
1.1 95

Create a scatterplot. Insert the trendline into the graph and show the regression equation.

-What is the regression equation? Identify the slope and y-intercept.
-What does the slope tell you?
-Determine and interpret the coefficient of determination.
-What would be the estimated selling price of a home that has one thousand square feet?

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