Solution to the Guided Study 1 Autumn
THE NEXT THIRTEEN QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose that you are interested in the relationship between the return rate on a stock in 2005, compared to
the return rate in 2004. You believe that the return rates in both years are positively correlated. A sample of
15 stocks yields the following regression results:
0
b
= 5.3,
1
b
= 1.04,
0
b
s
= 1.79,
1
b
s
= 0.2163,
2
R
=
0.64, and MSE = 35.4.
1.
How would you slope coefficient
1
b
?
ANSWER:
For every 1% increase in rate of return in 2004, we would expect the return rate in 2005 to
increase, on average, by 1.04%.
2.
What is the least squares regression line?
ANSWER:
ˆ
y
= 5.3+1.04
X
3.
What is the predicted value of
Y
when
X
= 5?
ANSWER:
ˆ
y
=5.3+1.04×5=10.5
4.
Calculate the error sum of squares.
ANSWER:
MSE
=35.4 =
2
SSE
n
=
13
SSE
SSE=35.4×13=460.2
5.
Calculate the total sum of squares.
ANSWER:
2
R
= 0.64 =1-
SSE
SST
=1-
460.2
SST
SST = 460.2 / 0.36 = 1278.33
6.
Calculate the regression sum of squares (explained).

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- Fall '19