Question

In: Statistics and Probability

Purchasing a car is a difficult decision. Car prices are a function of many variables such...

Purchasing a car is a difficult decision. Car prices are a function of many variables such as mileage, age, foreign or domestic manufacture and engine technology utilized. Develop and run the following multiple regression model:

  1. Interpret the beta coefficient (slope)s of all slopes: mileage, age, dummy engine and dummy foreign
  2. Interpret R squared value of the model and root mean squared error (RMSE)
  3. Would mileage and age influence your decision based on the statistical output for this sample data?
  4. Would the price of a car be raised if a car were of foreign make and used V6 engine technology?

What will the expected price of a car be in the lemon market if the age of a car was 8 years, with 9,000 miles on it, is of foreign make and with V6 engine?

Use Car Price ($) Mileage (Miles) Age (Years) Dummy Engine: V6 Technology=0, Not V6 Technology=1 Dummy Foreign: US=0, Foreign=1
26900 18000 10 1 1
24995 18500 11 0 1
23998 18670 12 0 1
22988 19000 17 1 0
21895 19020 16 0 0
20995 19540 18 1 0
19995 20001 19 0 0
19995 20025 19 0 0
18995 21000 18 0 0
18975 21250 17 0 0
17999 22000 17 0 0
17995 22134 18 0 0
17995 22345 18 0 0
16950 23450 19 1 0
16922 23540 20 0 0
16796 23780 20 1 0
15988 24000 21 0 1
14995 24670 22 0 1
14995 25000 23 1 1
14990 25009 23 1 1
13877 26001 24 0 1
11995 27001 15 0 1
11495 27250 16 0 1
10990 28000 17 0 1

Solutions

Expert Solution

The output is:

R² 0.963
Adjusted R² 0.957
R   0.981
Std. Error   862.818
n   24
k   3
Dep. Var. Use Car Price
ANOVA table
Source SS   df   MS F p-value
Regression 38,74,23,371.9349 3   12,91,41,123.9783 173.47 1.75E-14
Residual 1,48,89,109.6901 20   7,44,455.4845
Total 40,23,12,481.6250 23  
Regression output confidence interval
variables coefficients std. error    t (df=20) p-value 95% lower 95% upper
Intercept 48,683.4807
Mileage -1.2494 0.0712 -17.539 1.30E-13 -1.3979 -1.1008
Age -148.9609 59.7737 -2.492 .0216 -273.6467 -24.2751
Dummy Engine 499.2701 412.3030 1.211 .2400 -360.7788 1,359.3191

(a) Use Car Price = 48,683.4807 -1.2494Mileage -148.9609Age + 499.2701Dummy Engine

(b) 96.3%

(c) Yes

(d) Yes

(e) Use Car Price = 48,683.4807 -1.2494Mileage -148.9609Age + 499.2701Dummy Engine Use Car Price = 48,683.4807 -1.2494*45000 -148.9609*10 + 499.2701*0 Use Car Price = $-9029.1283.

orchestra answered 2 years ago
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