2. Linear Regression Consider the following return of the Performance Fund and t
ID: 3146187 • Letter: 2
Question
2. Linear Regression Consider the following return of the Performance Fund and the Excess Return on the Market Index for the same yeair: Table 1: Excess Return on the Market Index and Return of the Performance Fund Year Market Fund 2012 13.717.8 201323.2 20146.9 2015 16.8 2016 12.3 39 12.8 24.2 17.2 2.1. Calculation: Use the Ordinary Least Squares procedure to find out if there is a relationship between the Performance Fund y and the Excess Return on the Market Index r! in 2017, what would be the expected return of the Performance Fund? results! 22. Calculation: If the Market is expected to have an Excess Return of 15% 2.3. Calculation: Estimate the Standard Errors of and and discuss yourExplanation / Answer
Solution a.
The linear Regression formula is given by
The data can be worked out as follows
x
y
x^2
x*y
Year
Market
Fund
2012
13.7
17.8
187.69
243.86
2013
23.2
39
538.24
904.8
2014
6.9
12.8
47.61
88.32
2015
16.8
25.2
282.24
423.36
2016
12.3
17.2
151.29
211.56
Total
72.9
112
1207.07
1871.9
The formula for regression is y = ax+b
The values a and b are calculated with the above values of x and y
Then
a=
-1.76113
b=
1.657142
Therefor the Linear Regression formula is
Y = -1.76113+1.657142x
With this formula, we recalucte the values
x
y
x^2
x*y
Calculated
Error
Year
Market
Fund
2012
13.7
17.8
187.69
243.86
20.94
-3.14
2013
23.2
39
538.24
904.8
36.68
2.32
2014
6.9
12.8
47.61
88.32
9.67
3.13
2015
16.8
25.2
282.24
423.36
26.08
-0.88
2016
12.3
17.2
151.29
211.56
18.62
-1.42
Total
72.9
112
1207.07
1871.9
112
0.00
Solution b.
For market Excess return 15%, the calculated Fund Value is 23.10
Solution c.
The standard errors are calculated with excel and is as follows.
Regression Statistics
Multiple R
0.966639
R Square
0.934391
Adjusted R Square
0.912521
Standard Error
3.044256
Observations
5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
-1.76113
3.939107
-0.44709
0.685118
-14.2971
10.77486
-14.2971
10.77486
1.657142
0.253523
6.536469
0.007278
0.85032
2.463964
0.85032
2.463964
Since the R square value is 93%, the result is a very good fit.
x
y
x^2
x*y
Year
Market
Fund
2012
13.7
17.8
187.69
243.86
2013
23.2
39
538.24
904.8
2014
6.9
12.8
47.61
88.32
2015
16.8
25.2
282.24
423.36
2016
12.3
17.2
151.29
211.56
Total
72.9
112
1207.07
1871.9
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.