Statistical Methods for Psychology

Then

Then

The confidence interval is 4.041 to 4.731, and the probability is .95 that an interval com-
puted in this way will include the level of symptoms reported by an individual whose
stress score is 10. That interval is wide, but it is not as large as the 95% confidence inter-
val of 3.985 5 Y 5 4.787 that we would have had if we had not used X—that is, if we had
just based our confidence interval on the obtained values of Y(and ) rather than making
it conditional on X.
I should note that confidence intervals on newpredicted values of Yare not the same as
confidence intervals on our regression line. When predicted for new values we have to take
into account not only the variation around the regression line, but our uncertainty (error) in
estimating the line. In Figure 9.6 which follows, I show the confidence limits around the

sY

4.041...Y...4.731

=4.386 6 .345

=4.386 6 1.984(0.174)

CI(Y)=YN 6 (ta> 2 )(s¿Y#X)

=0.173 1 1.017=0.174

s¿Y#X=0.173

B

11

1

107

1

(10 2 21.290)^2

(106)156.05

s¿Y#X=sY#X

B

11

1

N

1

(Xi 2 X)^2

(N 2 1)s^2 X

Section 9.9 Confidence Limits on Y 267

Figure 9.6 Confidence limits around the regression of log(Symptoms) on Stress

4.2

0 10 20

Stress score

30 40 50 60

4.4

4.6

Log of Hopkin’s symptom checklist score

4.8

5.0