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 $R^2=0\mathrm{.}108,$ or $10\mathrm{.}8\%,$ which is a small valoe way less than $100\%.$ This means that the single independent variable, the market return, Rue does sof explain the return of an individual stock or portfolio very well in this simple linear regression model. Researchers have been developing new methodologies to add other independent veriables to better capture the relationship between returns of an individual asset and the measares of these independent variables. Fama and French $(1992){?}^1$ develop a three$-$factor model by adding two other variables pothe.basis. of the CAPM.

The model is in a form of: $R={}_1{R}_M{}_{2}SMBHML$ where $R$ is the returns of an individual finascial asset $($i$.$e a stock of a portfolio$),$ Ruvis the market return $($such as the S