I have data on about 8000 persons and I am trying to find independent predictors of a health outcome variable (yvar). The predictor variables are age, gender, height, city and 3 other predictor variables (xvar1, xvar2, xvar3). Some are continuous while others are categorical. The categorical variables are kept as such and not converted to numbers (e.g. 'M' and 'F' are levels in gender). The outcome variable (yvar) is continuous.
If I use following code in R (applying all interactions):
I get 5 of these 7 to be with $p<0.05$ (many are much less than 0.05) and overall $R^2$ of 0.11
On using following code:
I get $R^2$ of 0.18 but NONE of the predictors has $p<0.05$
What do I conclude from this? Should I or should I not use interactions? What is the best way to analyze such data?
Also, should I use one of above formats or following format:
These produce only 2-way interactions and not all combination interactions as in second format.