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I have a linear regression with multiple independent variables. One of the variables is binary. If the parameter estimates are positive or negative, does it share the same positive/negative relationship with the dependent variable as a continuous variable? So would the binary variable with a 1 value have higher dependent variable value than those with a 0 value if it was a positive relationship?

Jrod
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  • Welcome to the site, @Jrod. Just for the sake of clarity, what do you mean by "binomial"? For example, do you mean that it's binary (the only values that exist for this variable are $0$ or $1$), or that these are counts of 'successes' out of some total number of trials with a given probability of success? – gung - Reinstate Monica May 03 '13 at 03:31
  • Yes, I meant binary. I have two different areas where the data was collected and have coded them as 1 or 0 and used it as an interaction term in my regression. However the variable by itself had a significant p value in some of my analyses. – Jrod May 03 '13 at 03:52
  • Hmmm. Can you edit your question? Do you have an interaction term in your model? If so, that's crucial information. – Peter Flom May 03 '13 at 10:32
  • I do have an interaction term. The equation works out to be be y=x*g+a+g where g is the binary variable. – Jrod May 03 '13 at 16:54

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Looks like you might be missing a term (model in comments)

$$y=x\cdot g+a+g$$

Not sure I follow the notation you're using, so correct me if I'm wrong: but it looks like you're saying (if $a$ is a constant, $x$ the continuous regressor and $g$ a binary variable). I interpret this as:

$$y = \alpha + \beta_1 g x + \beta_2 g$$

This would fit a flat line (no slope) where $g=0$. I would suggest trying

$$y = \alpha + \beta_1 g x + \beta_2 g + \beta_3 x$$

so that if $g=0$ the slope changes rather than goes horizontal.

To answer your original question in a very simple model:

$$y = \beta g$$

Then $\beta > 0$ implies a positive relationship with the dependent variable. The same is true if you add more terms in.

The interpretation would get more complicated if you add interaction terms (it would help to see more detailed output from your model).

gung - Reinstate Monica
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