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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....