$[$Refer to q$3.$xlsx$]$ A capital asset pricing model $($CAPM$)$ describes the relationship between the excess return of an individual asset $($in decimal place$)$ and the market excess return $($in decimal place$).$ We will construct a simple linear regression of the monthly excess return of Tesla $(Y)$ on the monthly excess market return $(x)$ from the last year. The two excess returns are listed in the excel file.

a$.$ Plot the scatter plot with a least$-$squares line.

b$.$ What is the $90\%$ confidence interval for ${}_1?$

c$.$ Interpret the $90\%$ confidence interval for ${}_1.$

d$.$ An analyst says that the performance of the asset matches with the market expectation if ${}_0=0.$ If ${}_0>0,$ it means the asset outperforms the market expectation, and we would like to test for that. Does Tesla outperform the market expectation at the significance level of $0\mathrm{.}1?$ Form the null and alternative hypothesis, calculate the test statistics and draw your conclusion.

e$.$ The analyst says that the asset is aggressive if ${}_1>1.$ Is Tesla aggressive at the significance level of $0\mathrm{.}05?$ Form the null and alternative hypothesis, calculate the test statistics and draw your conclusion.