Pearson Correlation Coefficient [r] & Linear regression equation

Linear regression equation

a prediction formula. Y' = a + bX Y' is estimated or predicted score. a is the intercept, value of Y' when X is zero or point where the line crosses the Y axis

Linear regression equation cont.

b is reg. Coefficient - it is the slope of best fitting line that describes rel. between X and Y or amount of change in Y associated w/ 1 unit of change in X can be positive or neg., depending on how X and Y vary Once you know a and b, you can calculate Y' for any value of X Reg. Coeff. is a Least Squares Estimate

Pearson Correlation Coefficient [r]

detects linear relationship bet.X and Y. Gives you info on direction of rel. [ + in same direction, - in opp. direction] and strength of rel.between variables [closer to 1 or -1, greater strength]

[r^2]

expresses strength of rel. also - represents proportion of Y var. that is accounted for by knowledge of linear rel. between X and Y.

Rel. between Regression and Correlation

Higher corr. Between two variables, the better you can predict one from the other. Corr. Between X and Y is to that between Y and Y'. Info. about Y' can be used to determine r squared.