Basic Analysis and Graphing - SAS

Chapter 4 Performing Bivariate Analysis 101
Fit Line and Fit Polynomial
Table 4.4 Description of the Summary of Fit Report (Continued)
RSquare Adj
Root Mean Square Error
Mean of Response
Observations
Adjusts the Rsquare value to make it more comparable over models with
different numbers of parameters by using the degrees of freedom in its
computation.
See “Statistical Details for the Summary of Fit Report” on page 125.
Estimates the standard deviation of the random error. It is the square root of
the mean square for Error in the Analysis of Variance report. See Figure 4.12.
Provides the sample mean (arithmetic average) of the response variable. This
is the predicted response when no model effects are specified.
Provides the number of observations used to estimate the fit. If there is a
weight variable, this is the sum of the weights.
Lack of Fit Report
Note: The Lack of Fit report appears only if there are multiple rows that have the same x value.
Using the Lack of Fit report, you can estimate the error, regardless of whether you have the right form of the
model. This occurs when multiple observations occur at the same x value. The error that you measure for
these exact replicates is called pure error. This is the portion of the sample error that cannot be explained or
predicted no matter what form of model is used. However, a lack of fit test might not be of much use if it
has only a few degrees of freedom for it (few replicated x values).
Figure 4.11 Examples of Lack of Fit Reports for Linear and Polynomial Fits
The difference between the residual error from the model and the pure error is called the lack of fit error. The
lack of fit error can be significantly greater than the pure error if you have the wrong functional form of the
regressor. In that case, you should try a different type of model fit. The Lack of Fit report tests whether the
lack of fit error is zero.
Table 4.5 Description of the Lack of Fit Report
Source
The three sources of variation: Lack of Fit, Pure Error, and Total Error.