Question

For questions #13-20, refer to the following: A linear regression analysis is used to find the relationship between the age (x) of a car and the value in 1,000's (y) of that car. A random sample of some Ford Taurus model cars are being used with the results below. age (x): 2 5 9 4 7 6 value in 1000's (y): 24.5 16.7 7.3 22.3 5.6 14.5

What is the value for SSxy?

What is the value for SSxx?

What is the value for SSyy?

What is the value of the correlation coefficient, r?

What % of the y-variable is directly related to the x-variable?

What is the equation of the regression line?

What is the value of a 4 year old Ford Taurus based on this linear regression analysis?

What is the predicted value of a 7 year old Ford Taurus based on this linear regression model?

Answer 1

Based on the above calculation:

13. The value for SSxy is -86.35

14. The value for SSxx is 29.5

15. The value for SSyy is 294.195

16.

The correlation coefficient r is calculated as follows:

The value of the correlation coefficient, r is -0.9269

17.

The coefficient of determination r2 = -0.9269^2 = 0.8591

Since coefficient of determination is 0.8592, 85.91 % of the y-variable is directly related to the x-variable.

18.

19.

Substituting x = 4 in regression equation, we get

y (in 1000's) = 31.2492 - 2.9271*4

y (in 1000's) = 19.5408

The value of a 4 year old Ford Taurus based on this linear regression analysis is 19540.8

20.

Substituting x = 7 in regression equation, we get

y (in 1000's) = 31.2492 - 2.9271*7

y (in 1000's) = 10.7595

The value of a 4 year old Ford Taurus based on this linear regression analysis is 10759.5