Previously it was noted that the LINEST command in Excel can find standard errors on the slopes and intercepts of graphs For some applications this is sufficient for example if one is trying to determine whether a slope is significantly different from zero one would typically see if the estimated slope is 2 standard errors away from zero two standard deviations is what typically corresponds to 95 confidence intervals when quantities are distributed normally which may or may not be the case but is still a decent rule of thumb However for some analyses finding the standard errors on the slope and intercept does not directly get the error on the final quantity of interest In such cases one may need to use the error propagation formulas see posted file to obtain the error in the quantity of interest Below is one highly relevant example for psychophysics studies obtaining error estimates on the point of subjective equality xm Recall that xm is obtained from the slope and intercept of the z vs x plot Thus xm is given by where we have used that the slope is given by 1 w Transforming this into an equation for xm gives where we denote the intercept of the z vs x plot by b and the slope by m Finally from the error propagation notes for multiplication or division relative errors add in squares or where xm indicates the absolute value of xm 1001ln 1 mxzxyww1intercept slope mmwxx mbxm 222 mmxbmxbm 22mmxbmxbm