Pearson-Product Moment Correlation Coefficient (r) A measure of the relation between x and y, but is not standardized To standardize, we divide the covariance by the size of the standard deviations. Given that the maximum value of the covariance is plus or minus the product of the variance of x and the variance of y, it follows that the limits on the correlation coefficient are + or – 1.0

Example: XY

Compute the regression coefficient, but using standardized scores X’Y’ b= Why?

Adjusted r From our example: =.75

= that proportion of the variance in y that is shared (accounted for) by x. Sometimes called the “ coefficient of determination.” Thus, r =.9 and =.81 Or x accounts for 81% of the variance in y. R =.2, thus=.04 or 4% R =.4, thus=.016 or 16% If on r is g times as large as a second r, then the proportion of the variance associated with the first r will be g(squared) times as great as that associated with the second. can also be misleading

Factors Affecting r Range Restrictions Heterogeneous Subsamples Outliers

Whole-Part correlations. This is were the score for variable x contributes to the score of variable y. Produces a + bias in r. Again, Correlation does not imply causality. Variables may be accidentally related, or both may be related to a third variable, or the may influence each other. Which is more informative, the slope of the regression line or the correlation coefficient?