Suppose a salary data set with predictors

experience X in years

Education coded 1 for diploma , 2 for degree, 3 for higher degree

Management M coded as 1 for a person with management responsibility and 0 otherwise.

Using dummy variable

E_{i1}=1 if ith person has diploma ,0 otherwise.

E_{i2}=1[if ith person has degree ,0 otherwise.

Then the regression line would be.

Code:

`Y=beta_0+beta_1X+beta_2E_1+beta_3E_2+beta_4M+epsilon`

- E=1,M=0

- E=1,M=1
- E=2,M=0
- E=2,M=1
- E=3,M=0
- E=3,M=1

Doesn't these 6 combinations look like the case where there's a interaction between E and M predictors. Why 6 equations?Shouldn't it be 2 equations for regardless of the education level if M=0 and if M=1.

At this stage of the book interaction is not considered.

What is the difference between these 6 combinations and when the interaction term [E=1*M=0] and [E=2*M=0] usage

My second question is,

For this regression line if coefficient of E1=-3000 then is it interpreted as

**For fixed level of experience, regardless of the management position, a higher degree is worth 3000 than a diploma**

is this a correct interpretation.