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Linear Correlation CoefficientAnother method to test the accuracy of your regression equation, is to calculate the linear correlation coefficient, r. The linear correlation coefficient accounts for differences in both the x and y values and then calculates an average residual for the entire regression. The linear correlation coefficient (r) can be any value between -1 to 1 and is given by the following equation.
When the linear correlation coefficient equals 1 or -1, all data values fall along the linear regression. When r = 0, the data values are scattered around the line of regression, forming a circular cloud. As r moves from 0 to +/- 1, expect the circular cloud of data values to elongate into an ellipse until they finally fall into a straight line. The following pictures compare scatter plots with their respective linear correlation coefficients.
Coefficient of DeterminationAnother method of measurement worth noting is the coefficient of determination. The coefficient of determination is the variance in (Y) that can be accounted for by knowing (X) and visa versa. It is calculated by taking r2. The coefficient of determination is on a scale of 0 to 1, with 1 being a perfect linear relationship.It is important to remember that some data sets have several dependent variables. In these situations, you cannot use a linear regression. Instead, you must use a multiple regression analysis. Although we will not discuss multiple regression analysis in this section, it is important that you are aware that it exists. Report technical/content problems here |
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