In August $2023,$ UPS union workers negotiated a new collective bargaining agreement that included huge pay raises for many employees, with the average delivery driver receiving annual compensation of roughly $$170,000$ in pay and benefits. The company announced in January $2024$ that it is laying off $12,000$ workers. Use the return data for UPS to estimate a four$-$factor $($Carhart$)$ pricing model.

a$.$ Write down the appropriate four$-$factor pricing model, i$.$e$.,$ one that includes only variables that are statistically significant at the $95\%(1\mathrm{.}96$ t$-$stat$)$ level along with the risk$-$free rate. Include a screenshot of the regression output or your excel file. $(10$ points$)$