The coefficient of determination is ...
What's all this variation stuff?
Every sample has some variation in it (unless all the values are identical, and that's unlikely to happen). The total variation is made up of two parts, the part that can be explained by the regression equation and the part that can't be explained by the regression equation.
Well, the ratio of the explained variation to the total variation is a measure of how good the regression line is. If the regression line passed through every point on the scatter plot exactly, it would be able to explain all of the variation. The further the line is from the points, the less it is able to explain.
The coefficient of non-determination is ...
The coefficient of non-determination was used in the t-test to see if there was significant linear correlation. It was the in the numerator of the standard error formula.
The standard error of the estimate is the square root of the coefficient of non-determination divided by it's degrees of freedom.
The following only works when the sample size is large. Large in
this instance is usually taken to be more than 100. We're not going
to cover this in class, but is provided here for your information. The
maximum error of the estimate is given, and this maximum error of
the estimate is subtracted from and added to the estimated value of y.