What percentage of the variation in the price of a used car can be explained by...

What percentage of the variation in the price of a used car can be explained by its age? Round your answer to a percentage with a one decimal digit precision, for credit.

	Age (years)	Price ($)
Mean	6.133	8,404
St. Dev.	3.378	3,334
r	-0.972

Data Set:

Age	Price
1	13990
1	13495
3	12999
4	9500
4	10495
5	8995
5	9495
6	6999
7	6950
7	7850
8	6999
8	5995
10	4950
10	4495
13	2850

Solutions

Expert Solution

Answer: We obtain the Multiple R-squared value for the regression of price on age. It comes out to be 0.9443. We know from the definition of Multiple R-squared, which is also called the coefficient of determination, that it explains the amount of variation in the response variable that is explained by the explanatory variable. Here age is the explanatory variable and price is the response variable. Thus, on seeing the value of R-squared we say that 94.4 % of the variation in the price of a used car can be explained by its age.

The answer is rounded to one decimal digit precision and is obtained using R-software. Code and output are attached below.

orchestra answered 1 year ago

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