# interpretation of Linear regression

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?

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 $$x_i$$.