Question

Car dealers across North America use the Kelley Blue Book to help determine the value of used cars that their customers trade in when purchasing new cars. However, the Blue Book does not include the car's odometer reading as an indication of the car's value, despite the fact that this is a critical factor for used car buyers. It seems reasonable to believe that the more miles a used car has been driven, the less one would be willing to pay for the car. To examine this issue, a used car dealer randomly samples 100 Toyota Camrys that were sold at auction during the past month Each car was in top condition, three years old, and equipped with only standard features. The dealer recorded the following two variables: the selling price of the car (in dollars) and the odometer reading (in thousands of miles). StatCrunch was used to create the output below: Alternative DF Stat P Value Parameter estimates: Parameter Estimate Std. Emr. Intercept 17240727 182 09258 Slope -65 B60B 4974639 00001 Predicted values X value 95% CI for men 95% P.L. for new 41 672 (14378.9375, 14548 063) (130089, 15116.032) For any numeric responses, round your answers to four decimal places a. Identify the two variables which were recorded determining which is the predictor and which is the response The predictor variable is odometer reading . The response variable is price b. Which of the following correlation coefficients is most likely for this data?--085 c. Using the correlation selected in part b, calculate and interpret this value 85 of the variability in price is explained by the linear relationship with odometer reading of the variability is unexplained d. The estimated regression equation y 66 8609x + 172407271 e. Interpret the slope in context: We expect the price of a used Toyota Camry to decrease by 66 36 when the odometer increases by one Titles f. Based on the scatteplor would it be appropriate to interpret the intercept!

Answer 1

a)

The predictor variable = odometer reading

The response variable =price

b)

correlation coefficient r = -0.85

c)

Here we have to calculate r2

So r2 = (correlation coefficient ) 2 = (-0.85)2 = 0.7225

r2 = 0.7225

it is the 72.25% of variability in price is explained by linear relationship with odometer reading.

27.75% of the variability is unexplained.

d)

The estimated regression y= -66.8609+17248.727*X

e)

we expect decrease in price of a used Toyota camry to decrease by 66.86 when the odometer increases by 1000 miles