# Thread: Regression coefficient for interaction

1. ## Regression coefficient for interaction

Hi!

I have a homework question that on the face looks rather simple to me, but I want to check with people who may have greater statistics knowledge than I!

With this regression:

var1 = β0 + β1var2 + β2var3 + β3(var2 × var3)

How many regression coefficients are used to represent var2 and how many are used to represent the interaction?

As far as I can tell, I would say one for both...or is there something about the interaction being representative of the individual variables in a regression?

Any help would be much appreciated!

Thanks,

smashing

2. ## Re: Regression coefficient for interaction

As long as neither are categorical with greater than 2 groups, I would agree.

3. ## Re: Regression coefficient for interaction

Thanks!

How does it change if some of the variables are indeed categorical with more than two groups?

Binary-categorical interaction: consider the following linear regression model: (Notice that
for simplicity, the variable with bold fonts represents a vector which can contain more than one
predictor.)
BMI = β0 + β1physact + β2nonwhite + β3(physact × nonwhite)

Binary-continuous interaction: consider the following linear regression model:
BMI = β0 + β1SBP + β2diabetes + β3(SBP × diabetes)

Categorical-continuous interaction: consider the following linear regression model: (Notice
that for simplicity, the variable with bold fonts represents a vector which can contain more than
one predictor.)
BMI = β0 + β1globrat + β2SBP + β3(globrat × SBP)

Continuous-continuous interaction: consider the following linear regression model:
BMI = β0 + β1glucose + β2SBP + β3(glucose × SBP)

I'm being asked how many coefficient terms represent the interaction, as well as globrat and physat.

Any help would be much appreciated!

Thanks,

smashing

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