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1/22/07 252corr (Open this document in 'Outline' view!) L. CORRELATION 1. Simple Correlation The simple sample correlation coefficient is [pic] or if spare parts [pic], [pic] and [pic] are available, we can say [pic] Of course, since the coefficient of determination is [pic][pic] , [pic] and it is often easier to compute [pic] and to give the correlation the sign of [pic] . But note that the correlation can range from +1 to -1, while the coefficient of determination can only range from 0 to 1. Also note that since the slope in simple regression is [pic] , [pic] or [pic] or [pic]. The last equation has a counterpart in [pic] , where [pic] is the population correlation coefficient, so that testing [pic] is …show more content…

Example: [pic] applicants are rated by [pic]officers. The ranks are below. [pic]Note that if we had complete disagreement, every applicant would have a rank sum of 10.5. [pic]. The Kendall Coefficient of Concordance says that the degree of agreement on a zero to one scale is [pic]. To do a test of the null hypothesis of disagreement [pic], look up [pic] in the table giving ‘Critical values of Kendall’s [pic] as a Measure of Concordance’ for [pic] and [pic], [pic]so that we accept the null hypothesis of disagreement.. Example: For [pic] and [pic] we get [pic], and wish to test [pic] Since [pic] is too large for the table, use [pic]. Using a [pic] table, look up [pic] . Since 9 is below the table value, do not reject [pic]. 4. Multiple Correlation If [pic]is the coefficient of determination for a regression [pic], then the square root of [pic] , [pic] is called the multiple correlation coefficient. Note that [pic] where [pic] is the sample variance of [pic], and that for large [pic], [pic]. 5. Partial Correlation (Optional) If [pic], its multiple correlation coefficient can be written as [pic] or [pic]. For example, in the multiple regression problem, we got three multiple correlation coefficients [pic], [pic] and [pic] If [pic] and we compute the partial correlation of [pic]we compute [pic] , the additional explanatory power of the third independent variable after the

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