Learning Statistics with R - A tutorial for psychology students and other beginners, 2018a

Observed Values
40 50 60 70 80 90
50 60 70 80
Fitted Values
Figure 15.12: Plot of the fitted values against the observed values of the outcome variable. A straight
line is what we’re hoping to see here. This looks pretty good, suggesting that there’s nothing grossly
wrong, but there could be hidden subtle issues.
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15.9.4 Checking the linearity of the relationship
The third thing we might want to test is the linearity of the relationships between the predictors and
the outcomes. There’s a few different things that you might want to do in order to check this. Firstly, it
never hurts to just plot the relationship between the fitted values Ŷi and the observed values Y i for the
outcome variable, as illustrated in Figure 15.12. Todrawthiswecouldusethefitted.values() function
to extract the Ŷi values in much the same way that we used the residuals() function to extract the ɛ i
values. So the commands to draw this figure might look like this:
> yhat.2 plot( x = yhat.2,
+ y = parenthood$dan.grump,
+ xlab = "Fitted Values",
+ ylab = "Observed Values"
+ )
One of the reasons I like to draw these plots is that they give you a kind of “big picture view”. If this plot
looks approximately linear, then we’re probably not doing too badly (though that’s not to say that there
aren’t problems). However, if you can see big departures from linearity here, then it strongly suggests
that you need to make some changes.
In any case, in order to get a more detailed picture it’s often more informative to look at the relationship
between the fitted values and the residuals themselves. Again, we could draw this plot using low
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