1. Supposehavethesamplelinearregressionfunction:weY = B, + B,X, +e,, Bo and B are OLS estimates, prove the followingequations hold:Ee, = 0а.%3Db. Se,x, = 0, x, is the deviation form of XiEeÝ, = 0c.d.Y = Y2. Suppose the sample size n=10, we have the following figures for thesample data:ΣΥ-1110; ΣΧ-1 680; ΣΧY -204200 |ΣΧ31 5400; ΣΥ-133300The representation of PRF is Y = b, +b,X, +u,, u, O iid N(0,4)The OLS estimates for the SRF is ß, and Ba. calculate B, and B with the above figures.b. calculate the standard error of B, and B-c. calculate the determination coefficient: R?d. construct 95% confidence interval for b, and b, respectively.e. conduct hypothesis test: HO: b, =0, H1: b, #0.f. conduct hypothesis test: HO: b, =1, H1: b, #1.

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1. Suppose have the sample linear regression function: we Y = B, + B,X,+e,, B, and B are OLS estimates, prove the following equations hold: Ee, = 0 a. b. Ze,x, = 0, x, is the deviation form of Xi Eef, = 0 с. d.

1. Suppose have the sample linear regression function: we Y = B, + B,X,+e,, B, and B are OLS estimates, prove the following equations hold: Ee, = 0 a. b. Ze,x, = 0, x, is the deviation form of Xi Eef, = 0 с. d.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. Suppose
have
the
sample
linear
regression
function:
we
Y = B, + B,X, +e,, Bo and B are OLS estimates, prove the following
equations hold:
Ee, = 0
а.
%3D
b. Se,x, = 0, x, is the deviation form of Xi
EeÝ, = 0
c.
d.
Y = Y
2. Suppose the sample size n=10, we have the following figures for the
sample data:
ΣΥ-1110; ΣΧ-1 680; ΣΧY -204200 |
ΣΧ31 5400; ΣΥ-133300
The representation of PRF is Y = b, +b,X, +u,, u, O iid N(0,4)
The OLS estimates for the SRF is ß, and B
a. calculate B, and B with the above figures.
b. calculate the standard error of B, and B-
c. calculate the determination coefficient: R?
d. construct 95% confidence interval for b, and b, respectively.
e. conduct hypothesis test: HO: b, =0, H1: b, #0.
f. conduct hypothesis test: HO: b, =1, H1: b, #1.

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