Problem Set 3
ECON 837
Prof. Simon Woodcock, Spring 2006
Due: Friday Feb 10
These questions are based on the simple regression model:
y
i
=
°
+
±x
i
+
"
i
(1)
E
[
"
i
]
=
0
; E
°
"
2
i
±
=
²
2
; E
[
"
i
"
j
] = 0
when
i
6
=
j:
(2)
1. [Warmup Question, 2005 Midterm] You are studying the relationship between house
size and selling price. Let
Y
i
be the selling price of house
i
(in thousands of dollars)
and
X
i
its area (in square feet). On a random sample of 20 observations, you compute:
P
i
Y
i
= 10525
:
8
P
i
²
Y
i
°
°
Y
³
2
= 218087
P
i
²
X
i
°
°
X
³ ²
Y
i
°
°
Y
³
= 594257
P
i
X
i
= 47193
P
i
²
X
i
°
°
X
³
2
= 4325691
(a) Compute the least squares estimates of
°
and
±
in the regression:
Y
i
=
°
+
±X
i
+
"
i
:
Assume that the
"
i
are independent and each is distributed
N
(0
; ²
2
)
:
(b) What does the least squares estimate of
±
tell you about the relationship between
house size and selling price?
(c) Compute
R
2
for this regression. What does this value of
R
2
tell you?
(d) Test the hypothesis that
±
= 0
at the 5% level of signi°cance (use one test of your
choice). Interpret the result of your test.
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 Spring '09
 Thewalt
 Physics, Least Squares, Regression Analysis, Yi, simple regression model

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