CORRELATION AND REGRESSION
Product Moment Correlation Coefficient, to test if there is a linear relationship between the variables. To quantify the strength of the relationship, we can calculate the correlation coefficient (r). Its numerical value ranges from +1.0 to -1.0. r > 0 indicates positive linear relationship, r < 0
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Correlation coefficient is a measure of the direction and strength of the linear relationship of two variables Attach the sign of regression slope to square root of R2: 2 YX ... Test statistic t test F test. Sample and population Regression equations estimated with sample data can
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iii. The correlation coefficient is bound by –1 and +1. The closer the coefficient to –1 or +1, the stronger is the correlation. iv. With the exception of the extremes (that is, r = 1.0 or r = -1), we cannot really talk about the strength of a relationship indicated by the correlation coefficient without a statistical test of significance. v.
Used to test (1) Hypotheses and to control for (2) Confounding Variables E.G.: Is there gender bias in the salaries of lawyers? • Point-Biserial Correlation (rpb) of Gender and Salary: rpb =0.4 Correlation between Dichotomous and Continuous Variable • But females are younger, less experienced, & have fewer years on current job 1.
Correlation between continuous and categorial variables •Point Biserial correlation – product-moment correlation in which one variable is continuous and the other variable is binary (dichotomous) – Categorical variable does not need to have ordering – Assumption: continuous data within each group created by the binary variable are normally