Interaction terms in regression-theory

#1
I am learning categorical variables and interaction terms in the regression course and there few things I don't understand.

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
Then in the book , 6 regression equations are considered as when

  • 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.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
I did not completely follow your post content or question. Perhaps you can reference the book. Maybe the authors were looking at counterfactuals or trying to examine the different estimates for the levels.