Basic Statistics

178 REGRESSION AND CORRELATION

Y

r=-l

**

I -*

1 *a*

X

r=+~ t

*

f

Y

X

r= +1

a*

I ** 0.

Figure 12.4 Scatter diagrams with T = -1 and T = +1.

Y

r=O

...

. ..*._ --.

• .', a, '. a
  a.. ,.:.* ,
  ..... .... '.:,'....... .....
  . -... -.

r=O

% t

**'

X

Figure 12.5 Scatter diagrams with T = 0.

that the correlation coefficient can be 0 and still there may possibly be a nonlinear
relation between the two variables. The correlation coefficient is a measure of the
linear relationship between X and Y.
Examining the magnitude of T cannot replace a look at the scatter diagram, but
it is a useful measure of the degree of linear relationship between two variables.
A value of T less than -.7 or greater than +.7 in a large set of data might be considered
to indicate a high degree of relationship. It can be seen from comparing the formulas
for T and b that they always have the same sign. A negative value of T indicates that
the regression line slopes downward. However, the size of r does not indicate the
size of the slope coefficient.