Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 185

The top portion of the output is similar to an ANOVA (analysis
of variance) table. This is because regression and analysis of variance
are very similar. The input with the regress command assumes
that the independent variable, weight , is continuous. This results
in a single degree of freedom for the Source Model. The remainder
of this table is similar to an ANOVA table. There is no F-test or
probability reported in the ANOVA table because this information
is presented elsewhere in this output. The F-test and probability
are presented along with the R 2 , adjusted R 2 , and the mean square
error (MSE), which is the square root of the Residual mean square
(MS). he R 2 is the square of the correlation coefficient discussed
previously and represents that portion of the total sum of squares
(SS) that is the Model SS. This value (90.8354996/135.604033) is
0.6699. The closer the R 2 value is to 1 the better the model fits the
data. he adjusted R 2 , as mentioned in Chapter 5, is an adjustment
to the R 2 and in this context does not have much meaning.
The bottom portion of the output lists several pieces of informa-
tion, the most important of which is the coefficients (Coef.). The value
for weight (7.690104) is the slope of the least squares estimate of the
linear equation for these data. The _cons (55.26328) represents the
Y-intercept. Substituting a hen weight between 4.4 and 5.9 lbs in the
equation and including the slope, it is possible to predict food con-
sumption. It is important to understand that substituting a hen weight
is only valid within the range of actual weights. The regression line is
invalid beyond this range because the function may be quite different
outside these numbers. This makes sense, particularly in this context,
if you think about it. For example, plugging in a 100-lb hen to find
out its food consumption makes no sense because there is no such
thing as a 100-lb chicken (at least I'm pretty sure there isn't, Foghorn
Leghorn not withstanding).
After conducting the regression analysis, it may be worthwhile to
examine the results to determine if the underlying assumptions are
correct. One of these assumptions is the residuals occur randomly and
independently of the underlying model. Stata has two commands that
show whether this is true, the rvpplot and rvfplot . The for-
mer plots the residuals against the predictor or X value in the linear
regression. The latter plots the residuals against the fitted or Y value.