Correlations and non-linear relations
 View the accompanying screencast: [1]

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 between 4 pairs of variables.
CORRELATIONS /VARIABLES = x1 y1.
CORRELATIONS /VARIABLES = x1 y2.
CORRELATIONS /VARIABLES = x1 y3.
CORRELATIONS /VARIABLES = x2 y4.

* Scatterplots 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.
```

What do the linear correlations and bivariate scatterplots indicate about the relationship between the following pairs?

1. X1 by Y1
• r = .82 is appropriate - a strong, linear relationship
2. X1 by Y2
• r = .82 is somewhat accurate, but really the relationship is curvilinear
3. X1 by Y3
• r = .82 is not appropriate - really there is a perfect linear relationship plus an outlier
4. X2 by Y4
• r = .82 is not appropriate - there is a restricted range for x2 and an outlier