# ECON 3210 Chapter Notes - Chapter 6: Econometrics, Null Hypothesis, Explained Variation

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178

CHAPTER 6

Exercise Solutions

Chapter 6, Exercise Solutions, Principles of Econometrics, 4e 179

EXERCISE 6.1

(a) To compute

2

R

, we need SSE and SST. We are given SSE. We can find SST from the

equation

2

()

ˆ13.45222

11

i

yyy SST

NN

Solving this equation for SST yields

22

ˆ( 1) (13.45222) 39 7057.5267

y

SST N

Thus,

2979.830

1 1 0.8612

7057.5267

SSE

RSST

(b) The F-statistic for testing 02 3

:0H

is defined as

( ) ( 1) (7057.5267 979.830) / 2 114.75

( ) 979.830/(40 3)

SST SSE K

FSSE N K

At

0.05 , the critical value is (0.95,2,37) 3.25F

. Since the calculated F is greater than

the critical F, we reject 0

H. There is evidence from the data to suggest that 20 and/or

30 .

Chapter 6, Exercise Solutions, Principles of Econometrics, 4e 180

EXERCISE 6.2

The model from Exercise 6.1 is 12 3

yxze

. The SSE from estimating this

model is 979.830. The model after augmenting with the squares and the cubes of

predictions 23

ˆˆ

and yy

is 23

12 3 1 2

ˆˆ

yxzyye

. The SSE from estimating

this model is 696.5375. To use the RESET, we set the null hypothesis 01 2

:0H .

The F-value for testing this hypothesis is

()

(979.830 696.5375) 2 7.1175

( ) 696.5373 (40 5)

RU

U

SSE SSE J

FSSE N K

The critical value for significance level 0.05

is (0.95,2,35) 3.267F

. Since the

calculated F is greater than the critical F we reject 0

H and conclude that the model is

misspecified.