Anon

Multiple Linear Regression 57

be roughly 4.53%. Moreover, as expected, the change will be in the oppo-
site direction to the change in interest rates—when interest rates increase
(decrease) the value of this sector decreases (increases). The regression coef-
ficient is statistically significant at the 1% level as can be seen from the
t-statistic and p-value. The R^2 for this regression is 6.5%. Thus although
statistically significant, this regression only explains 6.5% of the variation
is the movement of the electric utility sector, suggesting that there are other
variables that have not been considered.
Moving on to the commercial bank sector, the estimated regression
coefficient is not statistically significant at any reasonable level of signifi-
cance. The regression explains only 1% of the variation in the movement of
the stocks in this sector.
Finally, the Lehman U.S. Aggregate Bond Index is, not unexpectedly,
highly statistically significant, explaining almost 92% of the movement in
this index. The reason is obvious. This is a bond index that includes all
bonds including Treasury securities.
Now let’s move on to add another independent variable that moves
us from the univariate case to the multiple linear regression case. The
new independent variable we shall add is the return on the Standard &
Poor’s 500 (S&P 500 hereafter). The observations are given in Table 3.2.

TAbLE 3.3 Estimation of Regression Parameters for Empirical Duration—Simple
Linear Regression

Electric

Utility Sector

Commercial

Bank Sector

Lehman U.S. Aggregate

Bond Index

Intercept

b 0 0.6376 1.1925 0.5308

t-statistic 1.8251 2.3347 21.1592

p-value 0.0698 0.0207 0.0000

Change in the Treasury Yield

b 1 –4.5329 –2.5269 –4.1062

t-statistic –3.4310 –1.3083 –43.2873

p-value 0.0008 0.1926 0.0000

Goodness-of-Fit

R^2 0.0655 0.0101 0.9177

F-value 11.7717 1.7116 1873.8000

p-value 0.0007 0.1926 0.0000