Standard Error Of Estimate

With the help of regression equations perfect prediction is practically impossible. For example, the revenue for the year from gasoline sales (Y) based on automobile registration (X) as of a certain date would no doubt be approximately fairly closely, but the prediction would not be exact to the nearest rupee nor probably to the nearest thousand rupees. What is needed, then, is a measure which would indicate how precise the prediction of Y is, based on X or, conversely, how inaccurate the prediction might be. The measure is called the standard error of estimate. The standard error of estimate, symbolized by Syx is the same concept as the standard deviation. The standard deviation measures the dispersion about an average, such as the mean. The standard error of estimate measures the dispersion about an average, such as the mean. The standard error of estimate measures the dispersion about an average line, called the regression line. The formula for calculating the standard error of estimate is:

S_yx =

S_yx  = σ_y 

Where S_yx = the standard error of regression of values from Y_c.

The formula is not convenient form the computational point of view because it requires the computation of (Y - Y_c ). A more convenient formula is

S_yx =

The standard error of regression of X values from X_c is

S_yx =    also  S_yx  = σ_y 


Also   S_yx  = 


S_yx = the standard error f regression of X values from X_c.

The standard error of estimate measures the accuracy of the estimated figures. The smaller the value of standard error of estimate, the closer will be the dots to the regression line and the better the estimates based on the equation for this line. If standard error or estimate is zero, then there is no variation about the line and the correlation will be perfect. Thus with the help of standard error of estimate it is possible for us to ascertain how good and representative the regression line is a description of the average relationship between the two series.

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