Page 159 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
Fitted Line Plot
*
+ 1.003 [ ] Study time * * 2
*
91.7%
R-Sq(adj)
90.7%
Figure 7-6:
The
parabola
appears to
fit the quiz-
score data
2
3
4
5
nicely. Quiz score 10 8 6 4 2 0 0 1 Quiz score = 9.823 − 6.149 [ ] Study time 6 S R-Sq 1.04825
Study time
To assess the fit of any model beyond the usual suspect, a scatterplot of
the data, you look at two additional items. Those items are the value of R 2
adjusted and the residual plots, which you typically check in that order after
assessing the scatterplot.
All three assessments must agree before you can conclude that the model
fits. If the three assessments don’t agree, you’ll likely have to use a different
model to fit the data besides a polynomial model, or you’ll have to change
the units of the data to help a polynomial model fit better. However, the latter
fix is outside the scope of intermediate statistics, and you probably will not
encounter that situation.
2
In the following sections, you take a deeper look at the value of R adjusted
and the residual plots and figure out how you can use them to assess your
model’s fit. (You can find more info on the scatterplot in the section “Starting
out with Scatterplots” earlier in this chapter.)
2
2
Examining R and R adjusted
2
Finding R , the coefficient of determination (see Chapter 5 for full details), is
2
like the day of reckoning for any model. You can find R on your regression
output, listed as “R-Sq” right under the portion of the output where the
coefficients of the variables are shown (see Figure 7-5).