# Random Sample

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Regression questions

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##### Solution Summary

The owner of Maumee Motors wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at Maumee Motors during the last year.

CAR AGE SELLING PRICE ($000) CAR AGE SELLING PRICE

1 9 8.1 7 8 7.6

2 7 6.0 8 11 8.0

3 11 3.6 9 10 8.0

4 12 4.0 10 12 6.0

5 8 5.0 11 6 8.6

6 7 10.0 12 6 8.0

1. If we want to estimate selling price based on the age of the car, which variable is the dependent variable and which is the independent variable?

2. Draw a scatter diagram.

3. Determine the coefficient of correlation.

4. Determine the coefficient of determination

5. Interpret these statistical measures. Does it surprise you that the relationship is inverse?

6. Determine the regression equation

7. Estimate the selling price of a 10 year old car.

8. Interpret the regression equation.

9. Determine the standard error of estimate.

##### Solution Preview

General calculations:

<br>let age : x, and price : y

<br>sum(x) = 107

<br>sum(y) = 712.9

<br>n =12

<br><x> = (=average or mean) = sum(x)/n = 107/12 = 8.91667

<br><y> = 6.90833

<br>sum(x^2) = 1009

<br>sum(y^2) = 615.29

<br>S2x = sum{(x - <x>)^2} = sum(x^2) - n*<x>^2 = 54.9166

<br>S2y = sum{(y - <y>)^2} = sum(y^2) - n*<y>^2 = 42.5892

<br>sum(xy) = 712.9

<br>Sxy = sum{(x-<x>)*(y-<y>)} = sum(xy) - n*<x>*<y> = ...

###### Education

- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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