Question

a statistics student is studying if there is a relationship between the price of a used car and the number of miles it had been driven. she collects data for 20 cars of the same model with different mileage and determines each cars price using a used car website. the analysis is given in the computer output. using the computer output, what is the predicted price for a car with 10,000 miles on the odometer? $22,347.20 $23,917.20 $24,157.20 $25,967.20 predictor coef se coef t - ratio p constant 24157.2 2164.1 2.965 0.046 mileage - 0.181 0.024 5.377 0.000 s = 3860.7 r - sq = 68.0% r - sq(adj) = 67.5%

Explanation:

Step1: Recall the linear regression formula

The linear regression formula is $\hat{y}=b_0 + b_1x$, where $b_0$ is the constant coefficient and $b_1$ is the coefficient for the predictor variable. From the computer - output, $b_0 = 24157.2$ (the coefficient of the constant) and $b_1=-0.181$ (the coefficient of mileage), and $x = 10000$ (miles on the odometer).

Step2: Substitute the values into the formula

Substitute $x = 10000$, $b_0 = 24157.2$, and $b_1=-0.181$ into $\hat{y}=b_0 + b_1x$.

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Answer:

$\$22,347.20$