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Some Regression doubts..

Say, I want to quantify the difference in the effect of BMI in onset age of diabetes for Hypertensive and non-hypertensive patients. I have done Multiple Linear Regression model with Age at onset of diabetes as outcome variable and BMI during diagnosis (continuous variable) and gender (binary) as predictor variables. ie. predicting onset age of diabetes from BMI adjusted for gender. (age_at_diag ~ bmi + gender)

This is done separately for Hypertensive diabetes patients and non-hypertensive diabetic patients. Now my questions are,

  1. Instead of doing it separately and comparing the coefficients can I add the hypertension variable (binary) in the above equation ie age_at_diag ~ bmi + gender + hypertension
  2. What is the difference between age_at_diag ~ bmi + gender + hypertension and age_at_diag ~ bmi + gender * hypertension (ie hypertension as an interaction term)

  3. How can you interpret the following MLR outputs

    Call:
lm(formula = aad ~ diab_bmi * hyper + gender * hyper, data = t2d)

Residuals:
    Min      1Q  Median      3Q     Max 
-31.431  -6.605  -0.479   6.511  41.083 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       57.14978    0.99077  57.682  < 2e-16 ***
diab_bmi          -0.25695    0.02781  -9.239  < 2e-16 ***
hyper1            11.58879    1.40013   8.277  < 2e-16 ***
genderMale        -1.99808    0.36447  -5.482 4.35e-08 ***
diab_bmi:hyper1   -0.19536    0.03877  -5.039 4.79e-07 ***
hyper1:genderMale -1.52097    0.52443  -2.900  0.00374 **

and

Call:
lm(formula = aad ~ diab_bmi + gender + hyper, data = t2d)

Residuals:
    Min      1Q  Median      3Q     Max 
-30.629  -6.667  -0.480   6.475  39.449 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 60.84250    0.70204   86.67   <2e-16 ***
diab_bmi    -0.35801    0.01941  -18.44   <2e-16 ***
genderMale  -2.76840    0.26246  -10.55   <2e-16 ***
hyper        4.34875    0.25437   17.10   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
arshad
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    When you refer to `gender * hypertension` as "an interaction term", you appear to be confusing it with `gender : hypertension` (which is the interaction). In R formulas `gender * hypertension` is the same as `gender + hypertension + gender : hypertension`. – Glen_b Apr 24 '13 at 14:10
  • Our site contains [over 100 threads](http://stats.stackexchange.com/search?tab=votes&q=interpretation%20interaction%20regression) concerning interpreting interaction terms in multiple regression! You will find a rich resource there for pursuing your inquiry. – whuber Apr 24 '13 at 14:59

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