Regression

In a regression line, for each x score you get a normal distribution of y scores with the mean on the regression line. See page 222.

Regression lines should not go beyond the original data points.

Error is regression is the difference between the average predicted Y and the actual Y.
(Y-Ybar). Observed minus expected. This is called standard error of the estimate, but it is the standard deviation using the Y and expected Y along (running) the regression line. Also known as coefficient of non-determination. (1-r squared).

Opposite of the error is the coefficient of determination (variability accounted for).

How much variance is error and how much is accounted for by a correlation with another variable?

Total variance = variance accounted for + error.

Variance accounted for is r squared (pearson r squared)

The connection between correlation and regression is r = a standardized slope of the regression line. r = b (s sub x / s sub y)