Basic Analysis and Graphing - SAS

Chapter 4 Performing Bivariate Analysis 103
Fit Line and Fit Polynomial
Analysis of Variance Report
Analysis of variance (ANOVA) for a regression partitions the total variation of a sample into components.
These components are used to compute an F-ratio that evaluates the effectiveness of the model. If the
probability associated with the F-ratio is small, then the model is considered a better statistical fit for the
data than the response mean alone.
The Analysis of Variance reports in Figure 4.12 compare a linear fit (Fit Line) and a second degree (Fit
Polynomial). Both fits are statistically better from a horizontal line at the mean.
Figure 4.12 Examples of Analysis of Variance Reports for Linear and Polynomial Fits
Table 4.6 Description of the Analysis of Variance Report
Source
DF
The three sources of variation: Model, Error, and C. Total.
The degrees of freedom (DF) for each source of variation:
• A degree of freedom is subtracted from the total number of non missing values
(N) for each parameter estimate used in the computation. The computation of
the total sample variation uses an estimate of the mean. Therefore, one degree of
freedom is subtracted from the total, leaving 50. The total corrected degrees of
freedom are partitioned into the Model and Error terms.
• One degree of freedom from the total (shown on the Model line) is used to
estimate a single regression parameter (the slope) for the linear fit. Two degrees
of freedom are used to estimate the parameters ( β 1 and β 2 ) for a polynomial fit
of degree 2.
• The Error degrees of freedom is the difference between C. Total df and Model
df.