Statistical Methods for Psychology

280 Chapter 9 Correlation and Regression

same purposes, although our variables contain enough random error that it is difficult to

make such precise statements. When we come to multiple regression in Chapter 14, you

will see again that the role of regression analysis is theory building.

9.13 The Role of Assumptions in Correlation and Regression

There is considerable confusion in the literature concerning the assumptions underlying

the use of correlation and regression techniques. Much of the confusion stems from the fact

that the correlation and regression models, although they lead to many of the same results,

are based on different assumptions. Confusion also arises because statisticians tend to

make all their assumptions at the beginning and fail to point out that some of these assump-

tions are not required for certain purposes.

The major assumption that underlies both the linear-regression and bivariate-normal

models and all our interpretations is that of linearity of regression.We assume that what-

ever the relationship between Xand Y, it is a linear one—meaning that the line that best fits

the data is a straight one. We will later refer to measures of curvilinear(nonlinear) rela-

tionships, but standard discussions of correlation and regression assume linearity unless

24

Rank distance

68 24

Rank distance

68

24

Rank distance

68 24

Rank distance

68

0

10

Distance

20

30

40

–1

0

Log distance

1

2

3

–0.2

–0.4

Residual

0.0

0.2

–5

Residual

0

5

Figure 9.7 Several plots related to distance of planets from the sun

linearity of
regression

curvilinear