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The ANOVA table tests the acceptability of the
model from a statistical perspective.
The Regression row displays
information about the variation accounted for by your
model.
The Residual row displays information about the
variation that is not accounted for by your model.
The regression and residual sums of squares are approximately
equal, which indicates that about half of the variation in
polishing time is explained by the model.
The significance value of the F statistic is less than 0.05,
which means that the variation explained by the model
is not due to chance.
While the ANOVA table is a useful test of the model's ability
to explain any variation in the dependent variable, it does
not directly address the strength of that relationship.
The model summary table reports the strength of the relationship
between the model and the dependent variable.
R, the multiple correlation coefficient, is the linear correlation
between the observed and model-predicted values of the dependent variable.
Its large value indicates a
strong relationship.
R Square, the coefficient of determination, is the squared value of
the multiple correlation coefficient. It shows that
about half the variation in time
is explained by the model.
As a further measure of the strength of the model fit, compare the
standard error of the estimate in the model summary table to the
standard deviation of time
reported in the descriptive statistics table.
Without prior knowledge
of the diameter of a new product, your best guess for the polishing
time would be about 35.8 minutes, with a standard deviation of
19.0.
With the linear regression model, the error of
your estimate is considerably lower, about 13.7.
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Checking the Model Fit |