# Thread: Interaction Terms in Linear regression

1. ## Interaction Terms in Linear regression

In R I used the linear regression call for three variables:

y, x, and c

Y and X are numeric where C is a dichotomous {0,1}. X and C are the regressors.

Since there was no linear relationship between X and Y when C = 0, I just ignored it and regressed the model using the subset of the sample where C = 1.

When I went back and regressed X + C + X*C, I obtained a linear model where B0 and B1 were identical to the previous B0 and B1 and the interaction coefficient was non-zero. This only bothers me because when I regressed only over C = 0, I obtained a constant relationship independent of X, but it did not equal the original constant + the contribution due to the interaction (in case I just programmed the index backwards)

Any clue what's going on?

For the actual output:

lm(formula = ovsat ~ lifesat, data = active.dataset)

Residuals:
Min 1Q Median 3Q Max
-1.97991 -0.25075 0.06956 0.34956 1.02009

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.01781 0.43395 6.954 4.15e-10 ***
lifesat 0.24053 0.09909 2.427 0.0171 *

lm(formula = ovsat ~ lifesat * status, data = dataset)

Residuals:
Min 1Q Median 3Q Max
-1.97991 -0.44380 0.06956 0.46903 1.64736

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.0178 0.5198 5.806 2.47e-08 ***
lifesat 0.2405 0.1187 2.026 0.044 *
status[T.2] 1.0276 0.7486 1.373 0.171
lifesat:status[T.2] -0.4188 0.1690 -2.479 0.014 *

lm(formula = ovsat ~ lifesat, data = inactive.dataset)

Residuals:
Min 1Q Median 3Q Max
-1.64264 -0.58380 -0.03186 0.55620 1.64736

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.0454 0.6101 6.631 1.52e-09 ***
lifesat -0.1783 0.1362 -1.309 0.193

2. ## Re: Interaction Terms in Linear regression

I didn't stare too hard at the above results, but skim and starting typing. Something like this is best portrayed using graphs. Graph the best fit line overlaid on a scatterplot for the continuous variables. Next, do the same thing, but dichotomize the IV based on the categorical variable. Now make the points on the graph coordinate with the group they are in and plot the lines generate from the interaction model.

This should help you understand what may be occurring. Also, feel free to post these graphs so we can also learn and evaluate the effects.

Thanks.

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