22 The Basics of financial economeTrics
From both the regression parameter b as well as the graphic, we see
that the two variables tend to move in the same direction. This supports
the previous finding of a positive correlation coefficient. This can be inter-
preted as follows. For each unit return in the S&P 500 index value, one can
expect to encounter about 1.06 times per unit return in the GE stock return.
The equivalent values for the parameters using weekly and daily returns are
b = 1.2421 and a = 0.0003 and b = 1.2482 and a = 0.0004, respectively.
Goodness-of-Fit of the Model
As explained in Appendix A, the correlation coefficient, denoted by rx,y , is a
measure of the linear association between x and y. We need to find a related
measure to evaluate the suitability of the regression line that has been
derived from the OLS estimation. For this task, the coefficient of determina-
tion, commonly denoted by R^2 , is introduced. This goodness-of-fit measure
calculates how much of the variation in y is caused or explained by the vari-
ation in x. If the percentage explained by the coefficient of determination is
FIGUre 2.4 Scatter Plot of Observations and Resulting Least Squares Regression Line
−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15−0.25−0.2−0.15−0.1−0.0500.050.10.150.2Monthly S&P 500 ReturnsMonthly GE Returns