Regression Analysis Fundamentals in Econometrics
Explore the key concepts of regression analysis, focusing on the conditional expectation function and population regression function. Learn about linear PRFs, the importance of stochastic disturbance terms, and the method of Ordinary Least Squares for estimating regression parameters.
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Presentation Transcript
Regression of Two Variable: Problem of Estimation Ekonometrika Al 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). 2
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 4
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. 5
The Leasts Squares Principle FIGURE - A 6
Least Squares Procedure The Least-squares procedure obtains estimates of the linear equation coefficients b0and b1, in the model. i b y 0 = + b x 1 i by minimizing the sum of the squared residuals ei. = = 2 i 2 y ( ) SSE e y i i 7
This results in a procedure stated as = = + 2 i 2 ( ( )) SSE e y b b x 0 1 i i 8
Least-Squares Derived Coefficient Estimators The slope coefficient estimator is n = ( )( ) x X y Y i i s = = 1 i Y b r 1 xy n s = 2 ( ) x X X i 1 i And the constant or intercept indicator is = b Y b X 0 1 9
The Assumptions Underlying The Method of Least Squares 10
TUGAS KE-2 Ditulis tangan pada kertas folio garis Dikumpulkan pada saat UTS 15
Perhatikan data berikut Year Income (x) Retail Sales (y) 9098 9138 9094 9282 9229 9347 9525 9756 10282 10662 11019 11307 11432 11449 11697 11871 12018 12523 12053 12088 12215 12494 1 2 3 4 5 6 7 8 9 5492 5540 5305 5507 5418 5320 5538 5692 5871 6157 6342 5907 6124 6186 6224 6496 6718 6921 6471 6394 6555 6755 Notes : 1. Hitung nilai koefisien b0 dan b1 2. Tulis persamaan regresinya 10 11 12 13 14 15 16 17 18 19 20 21 22 16
