waigaK

2020-11-01

The value of s alone doesn't reveal information about the form of an association. Sketch a scatterplot showing a nonlinear association with a small value of s and a second scatterplot showing a linear association with a large value of s.

comentezq

Step 1
The standard error of the estimate s (or standard deviation of the residuals) represents the average error of predictions, thus the average deviation between actual y-values and the predicted y-values.
First, we sketch a scatterplot with a linear association and a large value of s.
For example, the following graph has a standard error exceeding 10, while there is no strong curvature in the scatterplot indicating a linear association.

Step 2
Next, we sketch a scatterplot with a nonlinear association and a smallvalue of s.
For example, the following graph has a smaller standard error that hte previous exercise, because the points vary lies about the sketched line.
Moreover, the relation is nonlinear as there is strong curvature present in the scatterplot.

Result: