Question

Area	Auto Sales	Household Income	Population
1	209779	34926	193.16
2	109630	30732	170.85		Chapter 5 Exercise 5
3	121088	31891	128.03		Auto Sales, Household income and
4	124236	27624	159.58		Population for 10 metropolitan areas
5	551804	34940	349.51
6	427903	30943	399.97		AS=Auto Sales
7	102270	30259	149.52
8	212743	30070	215.77
9	353518	33470	308.94
10	115931	27875	162.12

Question 1. Download the data and develop a multiple-regression model for auto sales as a function of population and household income for 10 metropolitan areas. Please use excel and show all work.

1. Estimate values for b₀, b₁, and b₂ for this model:
   AS = b₀ + b₁ (INC) + b₂ (POP)
2. Are the signs you find for the coefficients consistent with your expectations? Explain.
3. What percentage of variation in AS is explained by this model?
4. What point estimate of AS would you make for a city where INC=23,175 and POP=128.7?

Answer 1

here is the R-code :

from the summary we see that estimated values of coeeficients b0, b1,b2 are

b0=-541917.75

b1=14.85

b2=1390.31

The fitted model is AS = -541917.75 + 14.85*INC + 1390.31*POP

c) here R2 = 0.9314

so variance explained by the model is 93.14%.

b) the estimate of b0 is negative and it is too high value ,it should not be negative in sign.this can be misleading.

d) the estimate of AS is -18836.1 which can not be negative as it is number of sales. so this may be the wrong sign of b0.