![]() All software provides it whenever regression procedure is run. Once a line of regression has been constructed, one can check how good it is (in terms of predictive ability) by examining the coefficient of determination (R2). A similar interpretation can be given for the regression coefficient of X on Y. It represents change in the value of dependent variable (Y) corresponding to unit change in the value of independent variable (X).įor instance if the regression coefficient of Y on X is 0.53 units, it would indicate that Y will increase by 0.53 if X increased by 1 unit. The coefficient of X in the line of regression of Y on X is called the regression coefficient of Y on X. We would then be able to estimate crop yield given rainfall.Ĭareless use of linear regression analysis could mean construction of regression line of X on Y which would demonstrate the laughable scenario that rainfall is dependent on crop yield this would suggest that if you grow really big crops you will be guaranteed a heavy rainfall. Here construction of regression line of Y on X would make sense and would be able to demonstrate the dependence of crop yield on rainfall. Choice of Line of Regressionįor example, consider two variables crop yield (Y) and rainfall (X). Often, only one of these lines make sense.Įxactly which of these will be appropriate for the analysis in hand will depend on labeling of dependent and independent variable in the problem to be analyzed. On the other hand, the line of regression of X on Y is given by X = c + dY which is used to predict the unknown value of variable X using the known value of variable Y. This is used to predict the unknown value of variable Y when value of variable X is known. The line of regression of Y on X is given by Y = a + bX where a and b are unknown constants known as intercept and slope of the equation. ![]() There are two lines of regression- that of Y on X and X on Y. ![]()
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