Problem $3($A Real Data Application$),$ Recalling in the simple linear regression model in Module $3,$ I gave a real data example using the Nobel$-$winning Capital Asset Pricing Model $($CAPM$).$ In that example, we obtained $R^0=0\mathrm{.}108,$ or $10\mathrm{.}8\%,$ which is a small value way less than $100\%.$ This means that the single independent variable, the market return, Ru$,$ does not explain the return of an individual stock or portfolio very well in this sipple linear regression model. Researchers have been developing new methodologies to add offer independent variables to better capture the relationship between returns of an individual asset and the measures of these independent variables. Fama and French $(1992)\text{'}$ develop a three$-$factor model by adding two other variables on the basis of the CAPM.

The model is in n form of: $R=R_2,5MB,MML$ where $R$ is the returns of an individual financial asset $($i$.$e$,$ a stock or a portfolio$),Ru$ is the market return $($such as the SAP $500\text{'}$s return as we used in the CAPM$),$ SMB is the Small $($market capitalization$)$ Minus Big, and the HML$,$ is the High $($book$-$to$-$market ratio$)$ Minus Low. Here Rw$,$ SMB$,$ and HML are the three factors. This is a typical multiple linear regression model.

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