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To see why OLS is logical, imagine a regression line running 6 units below one data point and 6 units above another point; it is 6 units away from the two points, on average. Now suppose a second line runs 10 units below one data point and 2 units above another point; it is also 6 units away from the two points, on average. But if we square the distances involved, we get different results: 6 2 + 6 2 = 72 in the first case, and 10 2 + 2 2 = 104 in the second case. So the first line yields the lower figure — the “least squares” — and is a more consistent reduction of the distance from the data points. (Additional methods, besides OLS, can find the best line for more complex forms of regression analysis.)

In turn, the typical distance between the line and all the points (sometimes called the “standard error”) indicates whether the regression analysis has captured a relationship that is strong or weak. The closer a line is to the data points, overall, the stronger the relationship.

Regression analysis, again, establishes a correlation between phenomena. But as the saying goes, correlation is not causation. Even a line that fits the data points closely may not say something definitive about causality. Perhaps some students do succeed in French class because they study hard. Or perhaps those students benefit from better natural linguistic abilities, and they merely enjoy studying more, but do not especially benefit from it. Perhaps there would be a stronger correlation between test scores and the total time students had spent hearing French spoken before they ever entered this particular class. The tale that emerges from good data may not be the whole story.

So it still takes critical thinking and careful studies to locate meaningful cause-and-effect relationships in the world. But at a minimum, regression analysis helps establish the existence of connections that call for closer investigation.

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Kelley Brown

March 16, 2010

I hope this kind of thing ("Explained")becomes a regular feature. Even if we learned about things like regression in school, it is easy to forget if you don't use it regularly.

thanks!

Ann Teve

July 15, 2011

Yes, this is written with exceptional clarity. Do continue this feature by this author.

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Charts and tables in this Emissions section of our website convert all greenhouse gas (GHG) emissions into CO 2 equivalents so they can be compared .

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