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In my upcoming social sciences dissertation, I am delving into testing hypotheses that explore the relationship between certain variables. In my framework, I've categorized these variables into two groups: the independent variables, which I refer to as the Xs, and the dependent variables, known as the Ys.

The core of my investigation is based on the presumption of a linear relationship between the Xs and Ys, typically represented by the equation Y = mX + C. Here, the Xs are count variables, specifically taking discrete values ranging from 0 to 10. The Ys, on the other hand, are continuous and can assume any numerical value, either positive or negative.

Initially, my approach was to apply linear regression to model this relationship. However, given the specific nature of the Xs as count variables, I've grown uncertain about the appropriateness of using linear regression. My concern is primarily about whether this approach may violate any underlying assumptions of the linear regression model, given the discrete nature of the independent variables.

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  • $\begingroup$ Which assumption of linear regression do you believe this could potentially violate? $\endgroup$
    – Firebug
    Commented Jan 23 at 12:16
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    $\begingroup$ You might want to look at splines to allow for potential nonlinearities in the response. Ideally, use theory to decide on your functional form. (Doing this in a "data-driven" way will invalidate your inference.) $\endgroup$ Commented Jan 23 at 12:23

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OLS regression makes no assumptions about the distribution of the independent variables. It makes assumptions about the errors, which we usually look at through the residuals.

The IVs can be continuous, categorical (either two categories or more), counts, or whatever. One way to remember this is to think of examples where OLS is used with (say) dichotomous variables (such as sex) or categorical ones (such as race) or whatever.

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    $\begingroup$ +1. For instance, in genetics one frequently models the number of particular alleles a person carries, which can be 0, 1 or 2. This presupposes that carrying two risk alleles yields twice the effect that a single one does. Which of course is not obvious, so other models (e.g., 0 against 1&2, or 0&1 against 2 are always possible). But there is nothing a priori against modeling counts as they are. $\endgroup$ Commented Jan 23 at 12:22

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