PS296 Chapter Notes - Chapter 10: Squared Deviations From The Mean
The Accuracy of Prediction:
The Standard Deviation as a Measure of Error
-sample standard deviation of Y is denoted as SY
-use to predict X when the X value is unknown
SY is defined as:
Variance is defined as
-the numerator is the sum of squared deviations from Y
The Standard Error of Estimate
-used to predict Y when X is known and the regression equation is known
-the error associated with this prediction will be a function of the deviations of Y about the predicted
point
-standard error of estimate is sometimes written SY.X to indicate that it is the standard deviation of Y
predicted from X
Document Summary
The standard deviation as a measure of error. Sample standard deviation of y is denoted as sy. Use to predict x when the x value is unknown. The numerator is the sum of squared deviations from y. Used to predict y when x is known and the regression equation is known. The error associated with this prediction will be a function of the deviations of y about the predicted point. Standard error of estimate is sometimes written sy. x to indicate that it is the standard deviation of y predicted from x. Its square (sy ) is called the residual variance/error variance. Once we compute the standard error of estimate, we can interpret it as a form of standard deviation r as a measure of predictable variability. When we start out with 2 variables (x and y) there is probably a great deal of variability in. Some of this variability is directly related to x/predictor variable, and some is just error.
