National open university of nigeria introduction to econometrics II eco 356



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Introduction to Econometrics ECO 356 Course Guide and Course Material
Introduction to Econometrics ECO 356 Course Guide and Course Material
INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
50



















…[2.19] Noting that
̅




̅





…[2.20] maybe rewritten as

̅
̅

…[2.21] and hence

̅
̅


…[2.22] Substituting for
and again noting that ∑


̅ we obtain








( ̅
̅) ̅
…[2.23] Separating the terms involving b
2
and not involving b
2
on opposite sides of the equation, we have

,(∑


) ̅
- ∑



̅̅̅̅
…[2.24] Dividing both sides by 2n,
0

(∑


) ̅
1


(∑



)
̅̅̅̅
…[2.25] Using the alternative expressions for sample variance and covariance, this maybe rewritten as

( ) ( )


( )
( )



…[2.26]
b
2
is from [2.23], b
1
is equally from [2.22]. Those who know about the second-order conditions will have no difficulty confirming that we have minimized RSS.
2.1.3.3.2 Alternative Expressions for b
2



INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
51 From the definitions of Cov(X, Y) and Var(X) one can obtain alternative expressions for b
2


( )
( )


(
̅)(
̅)



(
̅)



(
̅)(
̅)


(
̅)







1 2
1
n
i
n
i
xy
x



 

…[2.27] where,

x
X
X
 

y
Y
Y
 

2.1.4.0 SUMMARY
In this unit, you are expected to have learnt the essentials and applications of the concept of simple regression analyses and its estimation.
2.1.5.0 CONCLUSION
In conclusion, the concept of simple regression analyses and its estimation are explained.
2.1.6.0 TUTOR-MARKED ASSIGNMENT
1.) A researcher obtaineddata on the aggregate expenditure on services Y, and aggregate disposable personal income X, both measured in N billion at constant prices, for each of the US. states and fits the equation

̂
̂
̂

The researcher initially fits the equation using OLS regression analysis. However, suspecting that tax evasion causes both Y and X to be substantially underestimated, the researcher



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