How are returns on common stocks in overseas markets related to returns in U.S.
ID: 3182788 • Letter: H
Question
How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard & Poor's 500-Stock Index and overseas returns by the annual rate of return on the Morgan Stanley EAFE (Europe, Australasia, Far East) index. Both are recorded in percents. Regress the EAFE returns on the S&P 500 returns for the 30 years 1971 to 2000. Here is part of the Minitab output for this regression. The regression equation is EAFE = 4.76 + 0.663 S&P.
"Analysis of Variance"
Source: DF SS MS F P
Regression: 1 3445.9 3445.9 9.5 0.005
Residual Error:
Total: 29 13598.3
What are the values of the regression standard error s and the squared correlation r 2 ? (Enter your answers to four decimal places.)
s =
r 2 =
Explanation / Answer
Solution:
From the given information, we have ANOVA table as below:
Source
DF
SS
MS
F
P
Regression
1
3445.9
3445.9
9.5
0.00
Residual Error
28
10152.4
362.6
Total
29
13598.3
The formula for regression standard error is given as below:
s = sqrt(SSE/(n – 2))
SSE = 10152.4
n = 30
(n – 2) = 30 – 2 = 28
s = sqrt(10152.4/28) = sqrt(362.5857143)
s = 19.0417
The formula for coefficient of determination or the value of R square is given as below:
R-square = SSR / SST
R – square = 3445.9/13598.3 = 0.253406676
R-square = 0.2534
Source
DF
SS
MS
F
P
Regression
1
3445.9
3445.9
9.5
0.00
Residual Error
28
10152.4
362.6
Total
29
13598.3
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