# Correlation/Regression

Correlation and regression is discussed in a number of different examples, illustrated a variety of uses.

• Sethi and Seligman's (1993) study of the correlates of optimism and religious fundamentalism looks at both simple and multiple correlation and regression. In particular, it looks at the averaging of correlation coefficients.
• Katz, Lautenschlager, Blackburn, & Harris (1990) looked at the correlation between performance on the SAT and performance on a set of similar questions for which students had not read the relevant passage.
• Seligman, Nolen-Hoeksema, Thorton, & Thorton (1990) looked at the correlation between optimism and improvement in performance following a perceived failure.
• For those who would like to generate two variables with a specified correlation between them, there is a very simple procedure that can be applied with any statistical package.
• If you want a whole set of variables with a specified set of correlations, check out the response that David Nichols wrote in response to such an inquiry. An SPSS program that implements his suggestion is available at CorrGen2.html.
• A nice program to calculate confidence limits on rho is available on the UCLA Statistics page.
• A lab exercise investigating correlation (as well as t and power) is useful. It assumes SPSS, but the program could be rewritten for a different software package. The lab is not really a correlation lab, but it h as a program that will be useful and it has elements of correlation.
• A good demonstration of how variable sample correlation coefficients can be can be found at SampDistCorr.html. It shows students that variability is part of the nature of things.
• If you are correlating variables (such as scores from twins or gay partners) where there is no ordering within a pair (e.g. either twin could be considered twinA or twinB), you want an intraclass correlation coefficient.
• The sampling distribution of regression coefficients (b and b) are described in a document named SampDistRegCoeff.pdf.

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