ECON 3210 Lecture Notes - Econometrics, Confidence Interval, Interval Estimation
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132
CHAPTER 5
Exercise Solutions
Chapter 5, Exercise Solutions, Principles of Econometrics, 4e 133
EXERCISE 5.1
(a) 23
1, 0, 0yx x
*
2i
x
*
3i
x
*
i
y
0 1 0
1
2 1
2 1 2
2 0
2
1
1
1
2
1
2
0 1 1
1 1 0
1 0 1
(b) 22
** **
**
22 33
13, 16, 4, 10
ii i ii i
yx x yx x
(c)
2
** * *
*
*
*
23 323
222
22
** *
*
23 23
13 10 4 0 0.8125
16 10 0
ii i ii i i
ii ii
yx x yx x x
bxx xx
2
** * ****
32 223
322
22 **
**
23 23
416130 0.4
16 10 0
ii i ii i i
ii ii
yx x yx x x
bxx xx
12233
1bybxbx
(d)
ˆ0.4, 0.9875, 0.025, 0.375, 1.4125, 0.025, 0.6, 0.4125, 0.1875e
(e)
2
2ˆ3.8375
ˆ0.6396
93
i
e
NK
(f) 2233 23
23 2222
22 33 2 3
()() 0
()()
ii ii
ii ii
xxxx xx
rxx xx x x
(g)
2
22 22
22 23
ˆ0.6396
se( ) var( ) 0.1999
()(1)16
i
bbxx r
(h) 22
ˆ3.8375 ( ) 16,
ii
SSE e SST y y
212.1625
12.1625 0.7602
16
SSR
SSR SST SSE R SST
Chapter 5, Exercise Solutions, Principles of Econometrics, 4e 134
EXERCISE 5.2
(a) A 95% confidence interval for 2
is
2 (0.975,6) 2
se( ) 0.8125 2.447 0.1999 (0.3233, 1.3017)bt b
(b) The null and alternative hypotheses are
02 12
:1, :1HH
The calculated t-value is
2
2
10.8125 1 0.9377
se( ) 0.1999
b
tb
At a 5% significance level, we reject 0
H if (0.975, 6) 2.447tt
. Since 0.9377 2.447
,
we do not reject 0
H.