Regression of Two Variable:Problem of Estimation

EkonometrikaAl Muizzuddin F

Review the key concept

• The key concept underlying regression analysis is the concept of the conditional expectation function (CEF), or population regression function (PRF)

• Our objective in regression analysis is to find out how the average value of the dependent variable (or regressand) varies with the given value of the explanatory variable (or regressor).

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• This book largely deals with linear PRFs, that is, regressions that are linear in the parameters. They may or may not be linear in the regressand or the regressors.

• For empirical purposes, it is the stochastic PRF that matters. The stochastic disturbance term ui plays a critical role in estimating the PRF. 3

• The PRF is an idealized concept, since in practice one rarely has access to the entire population of interest. Usually, one has a sample of observations from the population. Therefore, one uses the stochastic sample regression function (SRF) to estimate the PRF

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The method of Ordinary Least Squares

• The method of ordinary least squares is attributed to Carl Friedrich Gauss, a German mathematician.

• Under certain assumptions the method of least squares has some very attractive statistical properties that have made it one of the most powerful and popular methods of regression analysis.

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The Leasts Squares Principle

FIGURE - A

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Least Squares Procedure

• The Least-squares procedure obtains estimates of the linear equation coefficients b0 and b1, in the model.

• by minimizing the sum of the squared residuals ei.

ii xbby 10ˆ

22 )ˆ( iii yyeSSE

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• This results in a procedure stated as

210

2 ))(( iii xbbyeSSE

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Least-Squares Derived Coefficient Estimators

• The slope coefficient estimator is

• And the constant or intercept indicator is

X

Yxyn

ii

n

iii

s

sr

Xx

YyXxb

1

2

11

)(

))((

XbYb 10

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The Assumptions Underlying The Method of

Least Squares

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11

12

13

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TUGAS KE-2

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• Ditulis tangan pada kertas folio garis• Dikumpulkan pada saat UTS

Perhatikan data berikut

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Year Income (x) Retail Sales (y)1 9098 54922 9138 55403 9094 53054 9282 55075 9229 54186 9347 53207 9525 55388 9756 56929 10282 587110 10662 615711 11019 634212 11307 590713 11432 612414 11449 618615 11697 622416 11871 649617 12018 671818 12523 692119 12053 647120 12088 639421 12215 655522 12494 6755

1. Hitung nilai koefisien b0 dan b12. Tulis persamaan regresinya

Notes :