For an example of calculating the regression line, let's use the tiny dataset from 9/18:

(1) Plot the data, checking whether a linear fit makes sense

:

(2a) Calculate the regression line: from summary statistics by converting to Z-scores or using the "hand formulas"

We end up with yhat = 0.95 + 0.809 x (that "yhat" should be a "y" with a "^" over it, to show that it's the predicted value).

(2b) Plot the regression line with the data.

(3) Now calculate the residuals.

and plot them:

We would like there to be no pattern.There might be an upside-down "U" pattern here, which suggests that a fitting a line might not have been best. With just four observations, however, it's hard to know.