![]() ![]() Yet doesn't the expected value entail that we must multiply this by the probability of occurring ? In general, you cannot expect that you will have enough data at each specific value of X, or it may be impossible to do so if X can take a continuous range of values. If so, as an example, if Y = obesity and X = age, if we take the conditional expectation E(Y|X=35) meaning, whats the expected value of being obese if the individual is 35 across the sample, would we just take the average(arithmetic mean) of y for those observations where X=35? In the probability model underlying linear regression, X and Y are random variables. Sorry if anything doesn't make sense or is obvious to anyone. If we don't assume the dependent variables are themselves random variables, since we don't obverse the probability, what do we assume they are? just fixed values or something? but if this is the case, how can we condition on a non-random variable to begin with? what do we assume about the independent variables distribution?.If $X$ represented something like the exchange rate, would this be classified as random? how on earth would you find the expected value of this without knowing the probability though? or would the expected value just equal the mean in the limit.if so, as an example, if $Y =$ obesity and $X =$ age, if we take the conditional expectation $E(Y|X=35)$ meaning, whats the expected value of being obese if the individual is $35$ across the sample, would we just take the average(arithmetic mean) of y for those observations where $X=35$? yet doesn't the expected value entail that we must multiply this by the probability of occurring ? but how in that sense to we find the probability of the $X$-value variable occurring if it represent something like age? Do we assume that both $X$ and $Y$ are random variables with some unknown probability distribution? it was my understanding that only the residuals and the estimated beta coefficients were random variables.It is my understanding that the linear regression model is predicted via a conditional expectation Okay so just a bit hazy on a few things, any help would be much appreciated.
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