This has come to be known as the 'spurious correlation' issue. If the dependent and independent variables, Y and X, are not independent, then regression or correlation analysis may well indicate they are correlated when in fact the relationship derives solely from the presence of a shared variable. This is a controversial topic which has generated considerable debate in the journals. SE b is the standard error of the slope.t is a quantile from the t-distribution for the chosen type I error rate (α) and n-2 degrees of freedom,.b is the slope of the regression of Y on X,.However, the confidence interval of this estimate is rather tedious to obtain as it requires computation of two further statistics, commonly known as D and H. b is the slope and a is the intercept of the regression on Y on X.This method is unbiased providing the usual assumptions of regression are met - in particular that X is measured without error.Īn unbiased estimate of X ( ) for a specified Y value (Y p) is obtained simply by reversing the equation. Instead one should use the method of inverse regression. If the X values are fixed and measured without error, it would not be valid to simply regress X on Y rather than vice versa as the assumptions of regression would not be met. Sometimes we may need to estimate X from Y, rather than the more usual procedure of estimating Y from X. n is the number of bivariate observations, and m is the number of replicates for the predicted mean.X p is the value of X for which Y is being estimated or predicted,.MS error is the mean square error which is Σ(Y − ) 2/ (n− 2) where is the expected value of Y for each value of X,.The error sums of squares is obtained by subtracting the regression sums of squares from the total sums of squares. The total sums of squares of the response variable (Y) is partitioned into the variation explained by the regression and the unexplained error variation. If errors are not normally and identically distributed, then a randomization test should be used. Analysis of variance is often the preferred approach, although one can also use a t-test to test whether the slope is significantly different from zero. Providing errors are normally and identically distributed, a parametric test can be used. There are several ways the significance of a regression can be tested.
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