Multiple Linear Regression 79
that of the CAPM beta. The conclusion from the regression results reported
in Table 3.9 is that there are factors other than the CAPM beta that explain
returns.
Key Points
■ (^) A multiple linear regression is a linear regression that has more than one
independent or explanatory variable.
■ (^) There are three assumptions regarding the error terms in a multiple
linear regression: (1) they are normally distributed with zero mean,
(2) the variance is constant, and (3) they are independent.
■ (^) The ordinary least squares method is used to estimate the parameters of
a multiple linear regression model.
■ (^) The three steps involved in designing a multiple linear regression model
are (1) specification of the dependent and independent variables to be
included in the model, (2) fitting/estimating the model, and (3) evaluating
TAbLE 3.9 Factors Found for U.S. Equity Market: Regression Results
U.S. Results (1979–1996)
Coefficient t-Statistic
Value Factors
Book/market 0.24 2.96
Earnings/price 0.40 5.46
Sales/price 0.28 4.25
Cash flow/price 0.38 5.28
Momentum Factors
Estimate revisions 0.56 13.22
Revisions ratio 0.55 14.72
Price momentum 0.61 7.17
Risk Factors
CAPM beta –0.17 –1.83
Residual risk –0.42 –4.05
Estimate uncertainty –0.33 –6.39
Source: Adapted from Exhibit 5 in Robert C. Jones, “The Active versus Passive
Debate: Perspectives on an Active Quant,” in Active Equity Portfolio Management,
ed. Frank J. Fabozzi (Hoboken, NJ: John Wiley & Sons, 1998), Chapter 3.