Example 1 To predict the asking price of a used Chevrolet Camaro, the following data were collected on the car’s age and mileage. Data is stored in CAMARO1. Determine the regression equation and answer additional questions stated later. Solution
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
The regression equation: Price =17499.1-1131.64Age-72.31MileageBe careful about the interpretation of the intercept (17499).Do not argue that this is the price of a used car with no mileagewhen its age is “zero”. Although such cars may exist (a car purchased and returned within a week with almost no mileage)might need to be re-sold as a used car. Yet, such values of Age and Mileage were not covered by the sample range!!.
Answer:Observe the Significance F. This is the p value for the F Test of the hypothesesH0: b1= b2 = 0H1: At least one b ¹0. Since the p value is practically zero, it is smaller than alpha. The null hypothesis is rejected, and therefore at least one b ¹0. The variable associated with this b is linearly related to the price, and the model is useful, thus contributes to predicting the asking price.
The linear regression equation:Price= 17357.38-1131.93Age-33.242Mileage- -2556.44Avg-3275.3Poor+775.64Dealer
bAge= -1131.93. In this model, For each additional year the asking price drops by $1132, keeping the rest of the variables unchanged.
bMile= -33.24. In this model, for each additional 1000 miles the asking price drops by $33.24, keeping the rest of the variables unchanged.
bAvg = -2556.44. In this model, the asking price for a car whose condition is average is $2556.44 lower than the asking price for a car whose condition is excellent, keeping the rest of the variables unchanged.
bPoor = -3275.3. In this model, the asking price for a car whose condition is poor is $3275.3 lower than the asking price for a car whose condition is excellent, keeping the rest of the variables unchanged.
bDeal = 775.64. In this model the asking price for a car sold by a dealer is $775.64 higher than this sold by an individual, keeping the rest of the variables unchanged.
In fact, the argument is even stronger. Since the t-statistic is negative
(-2.79), the rejection region is at the left hand tail of the distribution,
so we have sufficient evidence to claim that bavarage<0. This means the
asking price of an “Avg. Condition” car is on the average $2556 lower than the asking price of an “Excellent condition” car.
The variable “Average” is equal to 1 when the car is in average conditions.The variable “Dealer” is equal to 0 when the car is sold by an individual.Prediction power of independent variable (are there linear relationships?)
Price=17357 – 1131.9(4) – 33.242(45) – 2556.4(1) + 775.64(0)