THE SAMPLE STANDARD ERROR OF ESTIMATE
We will need a value for (Fe in deriving regression inferences. This population
value is a standard deviation which measures variations of points above and below the population regression line. Since we do not know the value of (Fe, we estimate it by Se, the sample standard error of estimate. The number Se is a standard deviation which measures the variations of sample points above and below the sample regression line. Specifically, s, is the standard deviation of the errors e we discussed earlier in the chapter. The formula defining Se is.
The divisor is n – 2 because, a stated in the last paragraph, two degrees of freedom are lost in simple linear regression inferences. Each error e is the difference between an observed y value and the y on the regression line directly above or below y, as illustrated in That is.
vious month’s sales were low. Thus, a value of Y is related to other values of
Y; so the independence assumption would not be valid. In brief, the assumptions of the normal regression model are that the Y values for every X are independent and normally distributed; and that every distribution has the same standard deviation Ue In a sample regression line, y = a + bx, a and b are, respectively, estimates of the population constant term A and the population slope B. In simple linear regression inferences, a consequence of using the two sample estimators a and b is that two degrees of freedom are lost. Thus jf we have n data points, the number of degrees of freedom is .
v = n – 2