I was reading about linear regressions on wikipedia and came across the mean and predicted response. I just wanted to clarify somethings. So suppose we have a simple linear regression model, is the result for the response variable $y_i$ for a given explanatory variable $x_i$ interpreted as the mean result for that specific $x_i$?

For example if the explanatory variable is temperature, and the response variable is # of ice cream sales, is $y_i$ interpreted as the number of sales that will occur at that specific temperature, or the average number of sales that will occur?


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The predicted mean response at $x_i$ (the estimated conditional expectation of $y_i$, $E(y_i|x=x_i)$ would be of the form $\hat{\alpha} + \hat{\beta} x_i$. This is sometimes denoted as $\hat{y}_i$.

In the example, $\hat{y}_i$ is the mean/expected number of ice cream sales at temperature $x_i$.


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