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Theory and Estimation of Regression Models Simple Regression Theory

Theory and Estimation of Regression Models Simple Regression Theory. Sumber : www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205. ppt ‎. Population Line:. E[Y] = B 0 +B 1 X. Y i = E[Y i ]+u i. u i. E[Y i ] = B 0 +B 1 X i. Xi.

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Theory and Estimation of Regression Models Simple Regression Theory

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  1. Theory and Estimation of Regression Models Simple Regression Theory Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  2. Population Line: E[Y] = B0+B1X Yi = E[Yi]+ui ui E[Yi] = B0+B1Xi Xi Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  3. Population Line: E[Y] = B0+B1X ^ Yi = Yi + ei Estimated Line: ^ ^ ^ Y = B0+B1X ei ui ^ ^ ^ Yi = B0+B1Xi E[Yi] Xi Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  4. ^ ^ ^ Y = B0+B1X ei ei ei ei ei ei Xi Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  5. Metode Ordinary Least Squares (OLS) • In the Ordinary Least Squares (OLS) method, the criterion for estimating β0 and β1 is to make the sum of the squared residuals (SSR) of the fitted regression line as small as possible i.e.:Minimize SSR = minimize = minimize = minimize Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  6. Metode Ordinary Least Squares (OLS) • Rumus estimator OLS : (5.12) (5.13) Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  7. Metode Ordinary Least Squares (OLS) • Garisregresi yang diestimasidenganmenggunakanmetode OLS mempunyhaiciri-ciri : • (i.e. the sum of its residuals is zero) • It always passes through the point The residual values (ei’s) are not correlated with the values of the independent variable (Xi’s) Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  8. Interpretasi Model Regresi • Assume, for example, that the estimated or fitted regression equation is: • or • Yi = 3.7 + 0.15Xi + ei Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  9. Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  10. Interpretasi Model Regresi Yi = 3.7 + 0.15Xi + ei • The value of = 0.15 indicates that if the average cotton price received by farmers in the previous year increases by 1 cent/pound (i.e. X=1), then this year’s cotton acreage is predicted to increase by 0.15 million acres (150,000 acres). Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  11. Interpretasi Model Regresi Yi = 3.7 + 0.15Xi + ei • The value of = 3.7 indicates that if the average cotton price received by farmers in the previous year was zero (i.e. =0), the cotton acreage planted this year will be 3.7 million (3,700,000) acres; sometimes the intercept makes no practical sense. Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  12. Mengukur Goodness of Fit: R2 • There are two statistics (formulas) that quantify how well the estimated regression line fits the data: • The standard error of the regression (SER)(Sometimes called the standard error of the estimate) • R2 - coefficient of determination Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  13. Mengukur Goodness of Fit: R2 • SER agakberbedadengansimpangan-baku (standard deviasi S) ei (olehderajatbebasnya): (5.20) Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  14. Mengukur Goodness of Fit: R2 • The term on the left measures the proportion of the total variation in Y not explained by the model (i.e. by X) • R2mengukurproporsidari total ragam Y yang dapatdijelaskanoleh model (yaitudijelaskanolehX) Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  15. Sifat-sifat Estimator OLS • The Gauss-Markov Theorem states the properties of the OLS estimators; i.e. of the: and They are unbiased E[B0 ]= and E[B1]= Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  16. Sifat-sifat Estimator OLS If the dependent variable Y (and thus the error term of the population regression model, ui) has a normal distribution, the OLS estimators have the minimum variance Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

  17. Sifat-sifat Estimator OLS • BLUE – Best Linear Unbiased Estimator • Unbiased => bias of βj = E(βj ) -βj = 0 • Best Unbiased => minimum variance & unbiased • Linear => the estimator is linear ^ ^ Sumber: www.aaec.ttu.edu/faculty/omurova/aaec_4302/.../Chapter%205.ppt‎

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