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Mini Cases: Simple Linear Regression: Mini Case 1: Estimating Car Prices Based on Mileage: Your car is acting up and you want to buy a new car. You started shopping and looking at different dealerships. You are interested in buying a 2012 Toyota Camry so you gathered some information about mileages and prices for different 2012 Toyota Camrys, which are shown in the following table: Mileage Price 22,500 $15,895 37,100 $14,485 54,700 $13,250 14,062 $17,010 25,100 $16,540 8,500 $16,500 15,440 $15,650 41,220 $14,950 a. Write down your estimated equation. b. Are your estimated coefficients significant? Explain. c. What will be the change in the price of the car if the mileage increases by 1,000? d. According to your estimate, what is the predicted average price of a 2012 Camry with 35,000 miles on it? If the dealer is asking for $14,500 for this car, is this a good deal for you? 1 |Page Multiple Linear Regression: Mini Case 2: Estimating Car Prices Based on Mileage and Age: Your car is acting up and you want to buy a new car. You started shopping and looking at different dealerships. You are interested in buying a Toyota Camry so you gathered some information about mileages, age and prices for different Toyota Camrys, which are shown in the following table: Age Mileage Price year 3 46386 15000 2013 3 26878 15891 2013 1 19442 17295 2015 1 2351 23990 2015 1 22159 17295 2015 3 32090 16500 2013 3 30505 16292 2013 4 24360 16795 2012 3 30474 16492 2013 5 18478 14490 2011 1 15881 21991 2015 3 18909 18000 2013 5 18478 14490 2011 5 58028 13390 2011 3 69406 14692 2013 a. Write down your estimated equation. b. What does each estimated coefficient mean? c. According to your estimate, what is the predicted average price of a 2013 Camry with 25,000 miles on it? If the dealer is asking for $15,500 for this car, is this a good deal for you? d. According to your estimate, what is the predicted average price of a 2015 Camry with 15,000 miles on it? If the dealer is asking for $19,500 for this car, is this a good deal for you? 2

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1.

Write down your estimated equation.

PRICE=17,485.18-0.0714(MILEAGE)

Are your estimated coefficients significant? Explain.

According to t-statistic:

t-stat = -5.06779

for 8 observations, df = n-1 = 7

t critical value for alpha=0.05 and df=7 is +/- 2.3646 (from t table)
therefore we reject the null hypothesis (H0: the coefficient of mileage is not significant). It means that the coefficient of mileage is significant.

For the constant term (intercept), t stat=39.91 which is greater than t-critical value. It means it is in the rejection area and we can say that the coefficient of intercept is significant.

According to p-value:

P values for the coefficients of intercept and mileage are 0.000 and 0.002 respectively. It means we reject the null hypothesis for both at 0.05 level and conclude that coefficients are significant....

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