Survey research and design in psychology/Tutorials/Correlation/Correlations and non-linear relations

The purpose of this exercise is to emphasise the importance of visualising bivariate relationships to check whether a linear correlation best represents the patterns in the data. CORRELATIONS /VARIABLES = x1 y1. CORRELATIONS /VARIABLES = x1 y2. CORRELATIONS /VARIABLES = x1 y3. CORRELATIONS /VARIABLES = x2 y4.
 * Data file: xy.sav
 * Syntax:
 * Correlations between 4 pairs of variables.

GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y1. GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y2. GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y3. GRAPH /SCATTERPLOT(BIVAR)=x2 WITH y4.
 * Scatterplots between 4 pairs of variables.

What do the linear correlations and bivariate scatterplots indicate about the relationship between the following pairs?
 * 1) X1 by Y1
 * 2) * r = .82 is appropriate - a strong, linear relationship
 * 3) X1 by Y2
 * 4) * r = .82 is somewhat accurate, but really the relationship is curvilinear
 * 5) X1 by Y3
 * 6) * r = .82 is not appropriate - really there is a perfect linear relationship plus an outlier
 * 7) X2 by Y4
 * 8) * r = .82 is not appropriate - there is a restricted range for x2 and an outlier