Question

A marketing researcher conducted a multiple regression analysis to explain how much customers spend on a company’s products (Amount Spent) as a function of four customer characteristics/variables: annual salary (Salary), number of children (Children), age (Age), and location (Location; rural or urban). Use the two partial ANOVA tables from regression analysis below to determine how much additional variation (as a percentage) in Amount Spent can be explained by Salary and Children, together, over-and-above Age and Location:

MODEL 1: Amount Spent = f(Age, Location)
SSE = 37,200 MSR = 11,600
MODEL 2: Amount Spent = f(Age, Location, Salary, Children)
SSE = 13,800 MSR = 11,650

a. 62.90%
b. 38.74%
c. 26.96%
d. 58.97%

Answer 1

The answer is "Option b"

Explanation:

In Model 1:

`\to SSR = 11600 * 2 = 23200\\\\\to SST = 23200 + 37200 = 60400\\\\\to R^2 = (23200)/(60400)`

`= 0.384106`

In Model 2:

`\to SSR = 11650 * 4 = 46600\\\\\to SST = 46600 + 13800 = 60400\\\\\to R^2 = (46600)/(60400) \\\\`

`= 0.771523`

The Additional variation value:

`= 0.771523 - 0.384106 \\\\ = 38.74\%`