Statistics: Regression Analysis and CAPM Model Application

This statistics assignment solution focuses on regression analysis and its application to the Capital Asset Pricing Model (CAPM). The assignment involves calculating excess market returns and excess returns on a preferred stock. It then proceeds to estimate the CAPM model through regression analysis, providing the regression results in an equation form. The solution further analyzes the beta coefficient, interpreting its value in terms of stock riskiness and aggressiveness. It also calculates and interprets the 95% confidence interval for the beta, the coefficient of determination (R-squared), and performs hypothesis testing to assess the stock's aggressiveness. The document concludes with the hypothesis testing results and a bibliography of cited sources.

Running head: STATISTICS
Statistics
Name of the Student:
Name of the University:
Author’s Note:

2STATISTICS
Table of Contents
Task 3...............................................................................................................................................3
Bibliography....................................................................................................................................6

3STATISTICS
Task 3
i) The excess market return that has been generated by the variable X = RM – RF is around -
1.65% and at the same time the return generated by the Rpreferred company stock – RF has been
around -1.09%. On a comparative basis it can be well seen that the preferred company stock has
generated a considerable amount of return for the investors and on the other hand side the market
has generated an excess return that is comparatively less than the company’s set of return.
ii) The Capital Asset Pricing Model can be well estimated by regressing the set of excess return
that has been generated or calculated on the evaluated preferred stock over the set of data for the
excess market return that has been taken into consideration for the company. The results of the
equation can be well shown below as:
y= 0.92+1.22*x
Please note that X in this case is the excess market rate of return generated.
iii) The estimated Beta Coefficient for the stock defining the slope coefficient shows or reflects
the riskiness or the aggressiveness of the stock in comparison to the set of market data return that
has been generated in the evaluated time period. The beta for the stock has been around 1.22
times stating that if the market moves by around 1 the stock is expected to move by around 1.22
times showing the aggressiveness of the stock.
iv) The 95% Confidence Interval well states that the value of the beta for the stock can lie
between 0.748 to around 1.696 times.

4STATISTICS
Coeffici
ents
Standa
rd
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Inter
cept
0.92032
4503
0.9079
0045
1.01368
4383
0.31494
3541
-
0.8970
3569
2.7376
847
-
0.8970
3569
2.7376
847
X=r_
m-rf
1.22228
5354
0.2367
2736
5.16326
182
3.10138
E-06
0.7484
2405
1.6961
4666
0.7484
2405
1.6961
4666
v) The coefficient of determination for the stock well states that how closely the data set are
related to each other which are when fitted to the regression line. The R2 or coefficient of
determination for the stock was calculated to be around 0.31 stating that the returns might not be
perfectly or closely related. The same can be well shown with the help of graphs and table shown
below:
-15 -10 -5 0 5 10
-30
-20
-10
0
10
20
Y=r_m-rf Line Fit Plot
Y=r_app-rf
Predicted Y=r_app-rf
X=r_m-rf
Y=r_app-rf
Regression Statistics
Multiple R
0.56116022
6
R Square
0.31490079
9
Adjusted R Square
0.30308874
4
Standard Error
6.34931828
5
Observations 60

5STATISTICS
vi) The hypothesis stock can be well calculated for the preferred stock can be well calculated
with the help of 5% significance level testing as shown below:
Ho: The beta value is not different from 1
Ha: The beta value is different from 1
P value is greater 0.05 so the Null Hypothesis cannot be rejected. On an overall basis the stock is
not aggressive according to the Test Done.
vii) The appropriate hypothesis test that would be done is as follows:
P value is greater than 0.05 so there is lack of evidence to reject the null hypothesis, hence the
null hypotheisis is retained.
Ho: the residuals are normally distributed
Ha: the residuals are not normally distributed

6STATISTICS
Bibliography
Chatterjee, S. and Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons.
Gunst, R.F., 2018. Regression analysis and its application: a data-oriented approach. Routledge.
Schroeder, L.D., Sjoquist, D.L. and Stephan, P.E., 2016. Understanding regression analysis: An
introductory guide (Vol. 57). Sage Publications.