Standard error, Applied Statistics

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Standard Error

The measure of reliability of the estimating equation that we have developed is given by standard error of estimate. The standard error of estimate represented by se is similar to the standard deviation as both are measures of dispersion. The standard error measures the variability, or scatter, of the observed values around the regression line.

The standard error of the estimate for a regression equation is given by

se = 2135_standard error.png

where,

= values of the dependent variable
384_standard error2.png = estimated values from the estimating equation that correspond to each Y value
n = number of data points used to fit the regression line

In the above equation you can observe the sum of the squared deviations is divided by n-2 and not by n. This is because we have lost 2 degrees of freedom in estimating the regression line. We used the sample to compute a and b.

Equation for calculating standard error of estimate is also given by formula

se = 374_standard error1.png

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