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STAT5044: Regression and ANOVA
Homework #1: solution
Problem# 1.
Refer to regression model. Assume that
X
= 0 is within the scope of
the model. What is the implication for the regression function if
β
0
= 0 so that the
model is
Y
i
=
β
1
X
i
+
±
i
? How would the regression function plot on a graph? The
implication of the model is that the regression line always goes through the origin.
The model only depends on slope.
Problem#2.
Refer to regression model. What is the implication for the regression
function if
β
1
= 0 so that the model is
Y
i
=
β
0
+
±
i
? How would the regression
function plot on a graph? This means that the line is horizontal line passing (0,¯
y
).
Problem# 3.
Consider the following model:
Y
i
=
βX
i
+
±
i
where
i
= 1
,...,n
,
±
i
are i.i.d with mean 0, variance
σ
2
.
(a) What estimator would you use to estimate
β
and
σ
2
? Please justify your answer
ˆ
β
=
∑
x
i
y
i
∑
x
2
i
ˆ
σ
2
=
∑
i
(
y
i

ˆ
βx
i
)
2
n

1
=
Y
t
(
I

H
)
Y
n

1
where,
H
=
X
(
X
t
X
)

1
X
t
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 Fall '11
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