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