Chapter 8 Regression and Correlation 335
Use the functions RUNS(range, center) and RUNSP(range,
center) to calculate the number of runs in a data set and the
corresponding p value for a set of data in the cell range, range,
around the central line center. StatPlus required.
Use the function DW(range) to calculate the Durbin-Watson test
statistic for the values in the cell range range. StatPlus required.
Correlation
The value of the slope in our regression equation is a product of the scale in
which we measure our data. If, for example, we had chosen to express the
temperature values in degrees Centigrade, we would naturally have a differ-
ent value for the slope (though, of course, the statistical signifi cance of the
regression would not change). Sometimes, it’s an advantage to express the
strength of the relationship between one variable and another in a dimen-
sionless number, one that does not depend on scale. One such value is the
correlation. The correlation expresses the strength of the relationship on a
scale ranging from 21 to 1.
A positive correlation indicates a strong positive relationship, in which
an increase in the value of one variable implies an increase in the value of
the second variable. This might occur in the relationship between height and
weight. A negative correlation indicates that an increase in the fi rst variable
signals a decrease in the second variable. An increase in price for an object
could be negatively correlated with sales. See Figure 8-20. A correlation of
zero does not imply there is no relationship between the two variables. One
can construct a nonlinear relationship that produces a correlation of zero.
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Figure 8-20
Correlations
positive correlation negative correlation
