what is residual standard deviation 
residual standard deviation is a statistical term used to describe the difference in standard deviations of observed values vs predicted values as shown by points in a regression analysis regression analysis is a method used in statistics to show a relationship between two different variables and to describe how well you can predict the behavior of one variable from the behavior of another residual standard deviation is also referred to as the standard deviation of points around a fitted line or the standard error of estimate understanding residual standard deviationresidual standard deviation is a goodness of fit measure that can be used to analyze how well a set of data points fit with the actual model in a business setting for example after performing a regression analysis on multiple data points of costs over time the residual standard deviation can provide a business owner with information on the difference between actual costs and projected costs and an idea of how much projected costs could vary from the mean of the historical cost data formula for residual standard deviation residual y y e s t s r e s y y e s t 2 n 2 where s r e s residual standard deviation y observed value y e s t estimated or projected value n data points in population begin aligned text residual left y y est right s res sqrt frac sum left y y est right 2 n 2 textbf where s res text residual standard deviation y text observed value y est text estimated or projected value n text data points in population end aligned residual y yest sres n 2 y yest 2 where sres residual standard deviationy observed valueyest estimated or projected valuen data points in population 