Serotoninl7

2021-11-25

You fit a CAPM that regresses the excess return of Coca-cola on the excess market return using 20 years of monthly data. You estimate $\alpha =0,72,\beta =1,37,{S}^{2}=20,38,{\sigma}_{X}^{2}=19,82\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}{\mu}_{x}=0,71$ .

What is the 99% confidence interval for$\beta$ ?

What is the 99% confidence interval for

Lupe Kirkland

Beginner2021-11-26Added 21 answers

Step 1

Sample Statistic = Slope of Regression i.e.$\beta$

$\beta =1.37$ , 99% confidence interval, $n=20$

$\alpha =1-\left(\frac{\text{Confidence interval}}{100}\right)$

$=1-\left(\frac{99}{100}\right)$

Degree of freedom$\left(df\right)=n-2$

$=20-2$

$=18$

As per the t distribution table, the critical value at df 18 is 2.552.

Standard Error or Standard Deviation$=\sqrt{19.82}=4.45197$

$\text{Margin of Error}=\text{Critical value}\times \text{Standard Error}$

$=2.552\times 4.45197$

$=11.36142$

Step 2

Confidence Interval$=\text{Sample Statistic}\pm \text{Margin of Error}$

$=1.37\pm 11.36142$

$\text{Upper Interval}=1.37+11.36412=12.73142$

$\text{Lower Interval}=1.37-11.36412=-9.99412$

Therefore, 99% confidence interval is -9.99412 to 12.73142

Sample Statistic = Slope of Regression i.e.

Degree of freedom

As per the t distribution table, the critical value at df 18 is 2.552.

Standard Error or Standard Deviation

Step 2

Confidence Interval

Therefore, 99% confidence interval is -9.99412 to 12.73142