# Answer following questions.

Show that bez is a ‘linearestimator.
It can be written as 2-1 W;li, where w; are random weights.
It can be written as 21-1 Wifi, where w; are random weights.
It can be written as wi/w2 + W3, where wi is linear in yı
and y2, and w2 is linear in Ii and X2, and w3 is a constant.
It can be written as !-1 W;yi, where w; are non-random
weights.
זי
It can be written as 2= w;li, where w; are non-random
weights.
Noting that two points
determine a line, If we
choose two points from
a sample of size N and
draw a line between
them, calling the slope
of this line the EZ
estimator of B2 in the
simple regression
model.
Algebraically, if the two
points are (X1,Y1) and
(x2, y2), the EZ
estimation rule is: bez
(y2-y1)/(x2-x1)
=
Question 3
5 pts
Referring to your
previous answer the
value of w2 is …
1
1
22 – 11
1
Y2 — Yi
Y2 — Yi
22 – 11
D:X1 (Xi – 7)(yi – 7)
2+1(xi – T)2
X1 – 41
Question 5
5 pts
The estimator bez is
unbiased because …
It will work for any sample size N > 1
E[bEz] = B2
bez = 32
E[12] = bez
Question 4
5 pts
What is the value of w3?
1
Y3 – Y2
1
1
C3
02
0
1
1
Y2 – 22
1

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