These both seem valid to me! Now, if you have multiple predictors (like SAT and height), then things get messy because you have to consider their covariance and stuff.
That reasoning as applied to SAT score would only be valid if LW selected its members based on their SAT score, and that reasoning as applied to height would only be valid if LW selected its members based on height (though it looks like both Thomas Kwa and Yair Halberstadt have already beaten me to it).
Edit: well, sort of. I think it depends on what information you’re allowing yourself to know when building your statistical model. If you’re not letting yourself make guesses about how the LW population was selected, then I still think the SAT thing and the height thing are reasonable. However, if you’re actually trying to figure out an estimate of the right answer, you probably shouldn’t blind yourself quite that much.
These both seem valid to me! Now, if you have multiple predictors (like SAT and height), then things get messy because you have to consider their covariance and stuff.
That reasoning as applied to SAT score would only be valid if LW selected its members based on their SAT score, and that reasoning as applied to height would only be valid if LW selected its members based on height (though it looks like both Thomas Kwa and Yair Halberstadt have already beaten me to it).
Cool, you’ve convinced me, thanks.
Edit: well, sort of. I think it depends on what information you’re allowing yourself to know when building your statistical model. If you’re not letting yourself make guesses about how the LW population was selected, then I still think the SAT thing and the height thing are reasonable. However, if you’re actually trying to figure out an estimate of the right answer, you probably shouldn’t blind yourself quite that much.