The manager of a used-car dealership is very interested in the resale price of u

Question

The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car (x) is important in determining the resale value (y). He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the response variable and the age of the car (in years) as the predictor variable. He found that the mean age of the used car in the sample is about 14 years and the standard deviation is about 2.6 years. The sample mean prices is 17 with a standard deviation of 4. The correlation between age of cars and the prices is about -0.4.

a)The slope of the regression line of yield of price on age is:

b)The intercept of the regression line of yield of price on age is:

c)The predicted value of the price of a used car which is 13 years old is:

d)Suppose a certain used car of age 13 years is sold at price 2.1. The residual value of the price is:

e)What percentage of total sample variation in price is explained by the model?

Explanation / Answer

a)slope of the regression line of yield of price on age is =r*Sy/Sx =-0.4*4/2.6=-0.62

b)  intercept =17-(-0.62)*14=25.68 ( please try 25.62 if this comes wrong)

c)predicted value =25.68-0.62*13=17.62 ( please try 17.56 if this comes wrong)

d)

residual =2.1-17.62=-15.52 (please try -15.46 if this comes wrong)

e) percentage of total sample variation in price is explained by the model=(r2)*100=16.0%

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