Basic Analysis and Graphing - SAS

104 Performing Bivariate Analysis Chapter 4
Fit Line and Fit Polynomial
Table 4.6 Description of the Analysis of Variance Report (Continued)
Sum of Squares
Mean Square
F Ratio
Prob > F
The sum of squares (SS for short) for each source of variation:
• In this example, the total (C. Total) sum of squared distances of each response
from the sample mean is 57,258.157, as shown in Figure 4.12. That is the sum
of squares for the base model (or simple mean model) used for comparison with
all other models.
• For the linear regression, the sum of squared distances from each point to the
line of fit reduces from 12,012.733. This is the residual or unexplained (Error)
SS after fitting the model. The residual SS for a second degree polynomial fit is
6,906.997, accounting for slightly more variation than the linear fit. That is, the
model accounts for more variation because the model SS are higher for the
second degree polynomial than the linear fit. The C. total SS less the Error SS
gives the sum of squares attributed to the model.
The sum of squares divided by its associated degrees of freedom. The F-ratio for a
statistical test is the ratio of the following mean squares:
• The Model mean square for the linear fit is 45,265.424. This value estimates the
error variance, but only under the hypothesis that the model parameters are zero.
• The Error mean square is 245.2. This value estimates the error variance.
The model mean square divided by the error mean square. The underlying
hypothesis of the fit is that all the regression parameters (except the intercept) are
zero. If this hypothesis is true, then both the mean square for error and the mean
square for model estimate the error variance, and their ratio has an F-distribution. If
a parameter is a significant model effect, the F-ratio is usually higher than expected
by chance alone.
The observed significance probability (p-value) of obtaining a greater F-value by
chance alone if the specified model fits no better than the overall response mean.
Observed significance probabilities of 0.05 or less are often considered evidence of a
regression effect.
Parameter Estimates Report
The terms in the Parameter Estimates report for a linear fit are the intercept and the single x variable.
For a polynomial fit of order k, there is an estimate for the model intercept and a parameter estimate for
each of the k powers of the X variable.