Regression and Correlation of Data Correlation: Correlation is a measure of the association between random variables, say X and Y. No assumption that one of these variables is known without error. Assume that X and Y are related linearly, so the usual correlation coefficient gives a measure of the linear association between X and Y, determined by This coefficient is often denoted simply by r.

Regression and Correlation of Data Correlation Coefficient: r =1: the points (xi,yi) are in a perfect straight line and the slope of that line is positive; r =-1: the points (xi,yi) are in a perfect straight line and the slope of that line is negative; r close to +1 or -1: X and Y follow a linear relation affected by random errors. r=0: there is no systematic linear relation between X and Y.

Regression and Correlation of Data Coefficient of determination: The coefficient of determination is the fraction of this sum of squares which is explained by the linear relation between and x given by regression of y on x. e.g. r 2 =0.997, which means 0.03% of the sum of squares of deviations in the y-direction from y bar is not explained by the regression. Example 43