The correlation coefficient indicates the degree of relationship between pairs of random variables. In this section we illustrate what can happen when one of the variables is binary and the other is user specified. Unmasking spurious correlation induced by apparent similarities in means is the subject of this section. We have two series, the Y variable is upward trending while the X variable is a 0/1 variable respesenting the two states of nature. Sometimes this kind of a variable (binary) is used to represent law changes, before and after.

A plot of the two series.

If we use regression we get a statistically significant relationship.

Once you use time series methods to augment the deficient regression model , the spurious significance goes away.

Finally, in first differences we conclude about the unmasking of the spurious relationship.

The data.

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