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A query consists of a request for an OLS regression of (almost) any 2 of the data files kept under my web pages. Once a dependent and independent variate are selected from the menus (NOTE: variates should be either both from the "cross-national" or both from the "Australian" columns) and the Submit button is clicked, the data is extracted, regressed, and the results returned. See the data dictionary for a brief definition of each variate, or read the online data file for other details.

Normally the OLS \beta ("slope") is tested against 0, and 90% confidence limits for \beta and \alpha ("intercept") are calculated. These and other basic statistics are returned, along with the dataset used. (At present the default and only method of supplying any missing values to the OLS is substituting the average value of a variate -- this is the "normal", if poor, method adopted in many statistics packages).

Example

GDP vs Participation Rate

Notes:

1. An r value near 1.0 shows the 2 variates have a close-to-linear relationship. But this isn't considered a very strong statistical test.
2. The r2 ("r squared") value shows the fraction of the variation of the dependent variate "explained" by its relationship (if any) with the independent variate. "Good" values for r2 probably start (it's sometimes a matter of taste) around 10%. If a relationship tests (via T-test and/or Spearman) as "significant", but the r2 is small, other factors are involved in determining the dependent variate.
3. Probabilities for accepting each alternative hypothesis (against H0: \beta == 0) are returned. If any test shows H0 is accepted at the tested confidence (90% by default) but any of these probabilities are greater than 75% (say), there is some reason to suspect a relationship between the 2 variates exists. I.e. if you re-run the OLS and set the confidence to any value less than the appropriate probability, you'll see a "reject H0" appear in the output.
4. A non-parametric Spearman correlation may be calculated for the data, in parallel with the OLS. The Spearman is tested at 5% and 1% (if independence is rejected at 5%) significance. If both the OLS T-tests and the Spearman test indicate the variates are related (i.e. they both reject H0) at 90% or better (say), there is some reason to suspect the variates are not independent.

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