Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman

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Introduction to Econometrics ECO 356 Course Guide and Course Material

INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
47 Table 2.1
X
Y
̂
e
1 3
2 5 We shall assume that the true model is
...[2.06] And we shall estimate the coefficients b
1
and b
2
of the equation using
̂
...[2.07] When X is equal to 1, according to the regression line
̂ is equal to (b
1
+ b
2
). When X
is equal to 2,
̂ is equal to (b
1
+ 2b
2
). Therefore, we can setup Table 2.1.0. So the residual for the first observation, e
1
, which is given by (Y
1
–
̂
1
), is equal to (3 – b
1
–
b
2
), and e
2
, given by (Y
2
–
̂
2
), is equal to (5 – b
1
– 2b
2
). Hence
(
)
(
)
...[2.08] Now we want to choose b
1
and b
2
so as to minimize RSS. To do this, we use the calculus and find the values of b
1
and b
2
that satisfy
…[2.09] Taking partial differentials of [2.08];

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
48
...[2.10] And
...[2.11] And so we have And Solving these two equations, we obtain b
1
= 1 and b
2
= 2, and hence the regression equation Just to check that we have come to the right conclusion, we shall calculate the residuals
e
1
= 3 – b
1
– b
2
= 3 – 1 – 2 = 0
e
2
= 5 – b
1
– 2b
2
= 5 – 1 – 4 = 0 Thus both residuals are equal to 0, implying that the line passes exactly through both points.

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