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I have a continuous dependent variable and one categorical independent variable (with three levels). For the three levels, I have 42, 33, and 45 observations respectively. So, in short, I have unequal sample sizes.

I want to run a linear model. But I am unsure how to account for the three levels' different sample sizes.

Is using weights in a linear model the right approach? If so, how to use assign them properly?

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    $\begingroup$ Welcome to Cross Validated! Is there a reason you believe you have to do something to account for the different sample sizes? There are advantages when it comes to experimental design in balancing the categories, and if what’s the budget to get more observations, sure, it could be reasonable to allocate that to observing members of the smallest class instead of the largest, but equal sample size is not an inherent assumption of regression on categories. $\endgroup$
    – Dave
    Commented Mar 27, 2023 at 12:06

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There are advantages when it comes to experimental design in balancing the categories, and if there is a budget to get more observations, sure, it could be reasonable to allocate that to observing members of the smallest class instead of the largest, but equal sample size is not an inherent assumption of regression on categories.

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