# Is it appropriate to suppress the intercept in a regression graph?

In the event of a non-significant interaction between X and M on Y, is it sound to suppress the intercept in the graph that illustrates the relationship between X and Y (X being significant). The moderator line in this case will pass through the origin and represent each level of the factor (M) at zero (i.e. male and female for gender).

SPSS provides this option under scatterplot.

I'm not sure there's a right answer to this, but maybe there are some ways of thinking about the issue that would be helpful. Not putting another regression line on your plot is a little like saying that the effect does not exist. Just because the effect is non-significant, however, does not necessarily mean that it doesn't exist. Thus, you could, in effect, be making a type II error. In the end, you must make a decision regarding what to believe. This decision should be influenced by the results of your analysis, but also by other things as well. For example, what was the prior probability of this effect--was it very plausible or were there strong theoretical reasons to expect it? (It can happen that you investigate something you don't think is real, such as someone else believes it and you don't, but typically people don't spend time studying things that they don't think are plausible.) Other relevant questions pertain to your study: Is there a confound or some idiosyncrasy of your study that might have caused the non-significant result? Do you have enough data to tell for sure? For instance, the estimated effect is never exactly zero, so what if that really is the true value, is it so small that you wouldn't care that it's not exactly zero anyway? Etc.

On another note, I gather you are making this graph for communicative / persuasive purposes. Thus, for example, if you really don't think the effect is real and you want to be able to show this to people, you may well want to plot both lines (possibly with observations from the two groups represented by different plotting symbols as well), so as to make it apparent that there is either no difference or one so trivial that no one should care. Or, that might clutter up you graph and make it harder for people to recognize your main message, and so you would leave it off for the sake of simplicity and clarity.

One of us is confused. If I understand correctly, your model (ignoring residuals) is

$Y = \alpha + \beta_1 \cdot M + \beta_2 \cdot X + \beta_3 \cdot M \cdot X$

The intercept is $\alpha$. It does not visually represent the interaction; the slope (the coefficient $\beta_3$) on $M \cdot X$ is the interaction. If $\beta_3$ is not significantly different from zero, it's sound to omit the interaction term from the regression, and to re-fit the model without it, which means that now your model looks like

$Y = \alpha + \beta_1 \cdot M + \beta_2 \cdot X$

If the remaining coefficients are all significant, the visual representation would have two lines.

One line for the observations where the factor is present (e.g., male):

$Y = \alpha + \beta_1 \cdot 1 + \beta_2 \cdot X = (\alpha + \beta_1) + \beta_2 \cdot X$

And one line for the observations where the factor is not present (e.g., female):

$Y = \alpha + \beta_2 \cdot X$

So that's why it doesn't make sense to me to ask about omitting the intercept $\alpha$ based on the value of $\beta_3$.

• You're right that $\alpha$ does not represent the interaction in any way. However, @AdheshJosh has asked a lot of questions about how to fit a model with 1 quantitative predictor and 1 qualitative predictor, how to interpret the interaction, etc. I am assuming that at this point that has all been done adequately and this is just an issue with the phrasing of the question. On the other hand, we should be cautious about fitting a model, dropping a non-significant term, refitting, etc. This is logically equivalent to an automatic search procedure and is associated with a lot of problems. – gung - Reinstate Monica Jan 8 '12 at 1:28