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Observaciones Yi Xi yi= Xi-X_barra xi=Yi-X_barra yi^2 xi^ 1 4.4567 6 -4.2180076923 -6 17.79158889237 36 2 5.77 7 -2.9047076923 -5 8.437326777751 25 3 5.9787 8 -2.6960076923 -4 7.268457476982 16 4 7.3317 9 -1.3430076923 -3 1.803669661598 9 5 7.3182 10 -1.3565076923 -2 1.84011311929 4 6 6.5844 11 -2.0903076923 -1 4.369386248521 1 7 7.8182 12 -0.8565076923 0 0.733605426982 0 8 7.8351 13 -0.8396076923 1 0.704941076982 1 9 11.0223 14 2.3475923077 2 5.511189643136 4 10 10.6738 15 1.9990923077 3 3.996370054675 9 11 10.8361 16 2.1613923077 4 4.671616707751 16 12 13.615 17 4.9402923077 5 24.40648808544 25 13 13.531 18 4.8562923077 6 23.58357497775 36 Suma 112.7712 156 Media 8.674707692 12 8.759860679 15. Beta2 131.7856 0. 182 Beta1 -0. sigma^2 9.6928096473 0. 11 var(Beta2) 0.8811645134 0. 182 Varianza muestral 4 -0. 0
1
i_gorro
∑▒𝑌𝑖 ∑▒𝑋𝑖 ∑▒ 〖𝑥 𝑖 𝑦𝑖 〗
(∑▒𝑌𝑖 )/𝑛(∑▒𝑋𝑖^ )/𝑛
(∑▒(𝑌_ 𝑖 𝑌− ̅)^( 2 ∑ ▒)/((𝑋𝑛−1_ 𝑖− )𝑋 ̅)^ 2 )/(𝑛−1)
r^2 9.6928096473 0.
var(Beta1) 2054 0. 2366 Pvalor_B1 -0.0144527473 0.
Pvalor_B2 0.7240967033 4.95788491E-
Yi_gorro Y_media (Yi_gorro-Ymedia)^ SCE (^) 4.330127473 8.67470769 18.875377286 95. 5.054224176 8.67470769 13. 5.778320879 8.67470769 8. 6.502417582 8.67470769 4. 7.226514286 8.67470769 2. 7.950610989 8.67470769 0. 8.674707692 8.67470769 0 9.398804396 8.67470769 0. 10.1229011 8.67470769 2. 10.8469978 8.67470769 4. 11.57109451 8.67470769 8. 12.29519121 8.67470769 13. 13.01928791 8.67470769 18. Yi Yi_gorro (Yi-Yi_gorro)^ SCR (^) 4.4567 4.33012747 0. 5.77 5.05422418 0.5123350305 9. 5.9787 5.77832088 0. 7.3317 6.50241758 0. 7.3182 7.22651429 0. 6.5844 7.95061099 1. 7.8182 8.67470769 0. Suma de cuadrados explicada Suma de cuadrado de los residuos
(∑▒𝑋_𝑖^
)/(𝑛∑▒𝑥_
𝑖^2 ) 𝜎^ 2
4
-1.
-0. 0
1
ui_gorro
𝑡=( 𝛽 ̂ _1− 𝛽_1 )/𝑒𝑒(𝛽_1 )
𝑡=( 𝛽 ̂ _ 2 − 𝛽_ 2)/𝑒𝑒(𝛽_2 )
𝑆𝐶𝐸=∑▒(𝑌 ̂ _𝑖−𝑌 ̅ )^
𝑆𝐶𝑅=∑▒(𝑌_𝑖−𝑌 ̂ _𝑖 )^2 =𝜇 ̂ _𝑖^
TABLA RESUMEN DE REGRESIÓN POR MCO
Observaciones 13 Modelo 95.4255185 1 95.425518502 R^2 0. Residuo 9.692809647 11 0.8811645134 Error tipico 0. Total 105.1183281 12 8.7598606791 F 108. F-pvalor 4.957885E- R^2 ajustado 0. 95% confianza Variables Coeficientes Desv. Std. t p-value Lim. Inf. Lim. Sup. Const -0.014452747 0.87462392 -0.0165245278 0.9871118467 1.910581513404 -1. X 0.724096703 0.06958134 10.406477866 4.9578849E-07 0.877244206132 0. Fuente de la variación Suma de cuadrados Grados de libertad Media de cuadrados
xiyi Yi_gorro ui_gorro ui^2_gorro Xi^2 Xiyi Yixi 25.3080462 4.33012747 0.12657253 0.0160206 36 -25.3080462 -26. 14.5235385 5.05422418 0.71577582 0.51233503 49 -20.3329538 -28. 10.7840308 5.77832088 0.20037912 0.04015179 64 -21.5680615 -23. 4.02902308 6.50241758 0.82928242 0.68770933 81 -12.0870692 -21. 2.71301538 7.22651429 0.09168571 0.00840627 100 -13.5650769 -14. 2.09030769 7.95061099 -1.36621099 1.86653247 121 -22.9933846 -6. 0 8.67470769 -0.85650769 0.73360543 144 -10.2780923 0 -0.83960769 9.3988044 -1.5637044 2.44517144 169 -10.9149 7. 4.69518462 10.1229011 0.8993989 0.80891838 196 32.8662923 22. 5.99727692 10.8469978 -0.1731978 0.02999748 225 29.9863846 32. 8.64556923 11.5710945 -0.73499451 0.54021692 256 34.5822769 43. 24.7014615 12.2951912 1.31980879 1.74189525 289 83.9849692 68. 29.1377538 13.0192879 0.51171209 0.26184926 324 87.4132615 81. 131.7856 112.7712 0 9.69280965 2054 131.7856 131. 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 f(x) = 0.724096703296703 x − 0. FRM Linear (FRM) FRP X Y 4 6 8 10 12 14 16 18 20 -0. 0
1
Cov(ui_gorro,Xi)
i_gorro 2 4 6 8 -0. 0
1
Cov(ui_gorr
i_gorro
∑▒ 〖𝑥 𝑖 𝑦∑▒𝑖 〗𝑌^ ̂_𝑖^ ∑▒𝜇 ̂^ _𝑖∑▒𝜇 ̂^ 𝑖^^2 ∑▒𝑋𝑖∑▒^^2 〖𝑋^ 𝑖^ ∑▒𝑦 𝑖〖^ 𝑌〗 𝑖 𝑥∑▒𝑖 〗^ 〖𝑋^ _𝑖
Xi-X_barra Xi*ui -6 0. -5 5. -4 1. -3 7. -2 0. -1 -15. 0 -10. 1 -20. 2 12. 3 -2. 4 -11. 5 22. 6 9. 0 -2.23821E- 14 16 18 20 FRP 4 6 8 10 12 14 16
Cov(ui_gorro,Yi)
Econometría Básica
Docente: Danny Moreno B.
Estimación por Mínimos
Cuadrados Ordinarios MCO
〖𝑌 𝑖 𝑥∑▒𝑖 〗^ 〖𝑋^ _𝑖
∑▒ 〖𝑋 𝑖 𝜇𝑖 〗
Observaciones Yi Xi yi= Xi-X_barra xi=Yi-X_barra yi^2 xi^ 1 4.4567 6 -4.2180076923 -6 17.79158889237 36 2 5.77 7 -2.9047076923 -5 8.437326777751 25 3 5.9787 8 -2.6960076923 -4 7.268457476982 16 4 7.3317 9 -1.3430076923 -3 1.803669661598 9 5 7.3182 10 -1.3565076923 -2 1.84011311929 4 6 6.5844 11 -2.0903076923 -1 4.369386248521 1 7 7.8182 12 -0.8565076923 0 0.733605426982 0 8 7.8351 13 -0.8396076923 1 0.704941076982 1 9 11.0223 14 2.3475923077 2 5.511189643136 4 10 10.6738 15 1.9990923077 3 3.996370054675 9 11 10.8361 16 2.1613923077 4 4.671616707751 16 12 13.615 17 4.9402923077 5 24.40648808544 25 13 13.531 18 4.8562923077 6 23.58357497775 36 Suma 112.7712 156 Media 8.674707692 12 8.759860679 15. Beta2 131.7856 0. 182 Beta1 -0. sigma^2 10.741368149 0. 11 var(Beta2) 0.9764880136 0. 182 Varianza muestral 4 -0. 0
1
i_gorro
∑▒𝑌𝑖 ∑▒𝑋𝑖 ∑▒ 〖𝑥 𝑖 𝑦𝑖 〗
(∑▒𝑌𝑖 )/𝑛(∑▒𝑋𝑖^ )/𝑛
(∑▒(𝑌_ 𝑖 𝑌− ̅)^( 2 ∑ ▒)/((𝑋𝑛−1_ 𝑖− )𝑋 ̅)^ 2 )/(𝑛−1)
r^2 10.741368149 0.
var(Beta1) 2054 0. 2366 Pvalor_B1 -0.9252923077 0.
Pvalor_B2 0.8 3.04265503E-
Yi_gorro Y_media (Yi_gorro-Ymedia)^ SCE 3.874707692 8.67470769 23.04 116. 4.674707692 8.67470769 16 5.474707692 8.67470769 10. 6.274707692 8.67470769 5. 7.074707692 8.67470769 2. 7.874707692 8.67470769 0. 8.674707692 8.67470769 0 9.474707692 8.67470769 0. 10.27470769 8.67470769 2. 11.07470769 8.67470769 5. 11.87470769 8.67470769 10. 12.67470769 8.67470769 16 13.47470769 8.67470769 23. Yi Yi_gorro (Yi-Yi_gorro)^ SCR 4.4567 3.87470769 0. 5.77 4.67470769 1.1996652393 10. 5.9787 5.47470769 0. 7.3317 6.27470769 1. 7.3182 7.07470769 0. 6.5844 7.87470769 1. 7.8182 8.67470769 0. Suma de cuadrados explicada Suma de cuadrado de los residuos
(∑▒𝑋_𝑖^
)/(𝑛∑▒𝑥_
𝑖^2 ) 𝜎^ 2
4
-1.
-0. 0
1
ui_gorro
𝑡=(𝛽 ̂ _1−𝛽_1)/𝑒𝑒(𝛽_1 )
𝑡=(𝛽 ̂ _2−𝛽_2)/𝑒𝑒(𝛽_2 )
𝑆𝐶𝐸=∑▒(𝑌 ̂ _𝑖−𝑌 ̅ )^
𝑆𝐶𝑅=∑▒(𝑌_𝑖−𝑌 ̂ _𝑖 )^2 =𝜇 ̂ _𝑖^
TABLA RESUMEN DE REGRESIÓN POR MCO
Observaciones 13 Modelo 94.37696 1 94.37696 R^2 0. Residuo 10.74136815 11 0.9764880136 Error tipico 0. Total 105.1183281 12 8.7598606791 F 119. F-pvalor 3.042655E- R^2 ajustado 0. 95% confianza Variables Coeficientes Desv. Std. t p-value Lim. Inf. Lim. Sup. Const -0.925292308 0.92071731 -1.0049689503 0.3365069971 1.101192826455 -2. X 0.8 0.07324834 10.921749783 3.042655E-07 0.961218500974 0. Fuente de la variación Suma de cuadrados Grados de libertad Media de cuadrados
xiyi Yi_gorro ui_gorro ui^2_gorro Xi^2 Xiyi Yixi 25.3080462 3.87470769 0.58199231 0.33871505 36 -25.3080462 -26. 14.5235385 4.67470769 1.09529231 1.19966524 49 -20.3329538 -28. 10.7840308 5.47470769 0.50399231 0.25400825 64 -21.5680615 -23. 4.02902308 6.27470769 1.05699231 1.11723274 81 -12.0870692 -21. 2.71301538 7.07470769 0.24349231 0.0592885 100 -13.5650769 -14. 2.09030769 7.87470769 -1.29030769 1.66489394 121 -22.9933846 -6. 0 8.67470769 -0.85650769 0.73360543 144 -10.2780923 0 -0.83960769 9.47470769 -1.63960769 2.68831338 169 -10.9149 7. 4.69518462 10.2747077 0.74759231 0.55889426 196 32.8662923 22. 5.99727692 11.0747077 -0.40090769 0.16072698 225 29.9863846 32. 8.64556923 11.8747077 -1.03860769 1.07870594 256 34.5822769 43. 24.7014615 12.6747077 0.94029231 0.88414962 289 83.9849692 68. 29.1377538 13.4747077 0.05629231 0.00316882 324 87.4132615 81. 131.7856 112.7712 1.59872E-14 10.7413681 2054 131.7856 131. 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 f(x) = 0.8 x − 0. FRM Linear (FRM) FRP X Y 4 6 8 10 12 14 16 18 20 -0. 0
1
Cov(ui_gorro,Xi)
i_gorro 2 4 6 8 -0. 0
1
Cov(ui_gorr
i_gorro
∑▒ 〖𝑥 𝑖 𝑦∑▒𝑖 〗𝑌^ ̂_𝑖^ ∑▒𝜇 ̂^ _𝑖∑▒𝜇 ̂^ 𝑖^^2 ∑▒𝑋𝑖∑▒^^2 〖𝑋^ 𝑖^ ∑▒𝑦 𝑖〖^ 𝑌〗 𝑖 𝑥∑▒𝑖 〗^ 〖𝑋^ _𝑖
- 7.8351 9.3988044 2. - 11.0223 10.1229011 0. - 10.6738 10.8469978 0. - 10.8361 11.5710945 0. - 13.615 12.2951912 1. - 13.531 13.0192879 0. - Yi Y_barra (Yi-Yi_gorro)^
- SCT 4.4567 8.67470769 17. - 5.77 8.67470769 8.4373267778 105. - 5.9787 8.67470769 7. - 7.3317 8.67470769 1. - 7.3182 8.67470769 1. - 6.5844 8.67470769 4. - 7.8182 8.67470769 0. - 7.8351 8.67470769 0. - 11.0223 8.67470769 5. - 10.6738 8.67470769 3. - 10.8361 8.67470769 4. - 13.615 8.67470769 24. - 13.531 8.67470769 23.
- Grados de libertad del modelo corregido
- DFE=n-p
- MCM=SCE/DFM 95. Grados de libertad del error
- MCE=SCR/DFE 0. Media de cuadrados explicados
- MCT=SCT/DFT DFT=DFM+DFE 8. Media de cuadrados de los resiudos
- F= MCM/MCE 108. Media de cuadrados totales
- Pvalor_F 4.95788491E-
- R cuadrado ajustado 0. - 𝑆𝐶𝑇=∑▒(𝑌𝑖−𝑌 ̅ )^2 =𝑦𝑖^ cuadrados Total
- ̅ )^2 =𝑦_𝑖^ - 7.8351 9.47470769 2. - 11.0223 10.2747077 0. - 10.6738 11.0747077 0. - 10.8361 11.8747077 1. - 13.615 12.6747077 0. - 13.531 13.4747077 0.
- Yi Y_barra (Yi-Yi_gorro)^
- SCT 4.4567 8.67470769 17. - 5.77 8.67470769 8.4373267778 105. - 5.9787 8.67470769 7. - 7.3317 8.67470769 1. - 7.3182 8.67470769 1. - 6.5844 8.67470769 4. - 7.8182 8.67470769 0. - 7.8351 8.67470769 0. - 11.0223 8.67470769 5. - 10.6738 8.67470769 3. - 10.8361 8.67470769 4. - 13.615 8.67470769 24. - 13.531 8.67470769 23.
- Grados de libertad del modelo corregido
- DFE=n-p
- MCM=SCE/DFM 116. Grados de libertad del error
- MCE=SCR/DFE 0. Media de cuadrados explicados
- MCT=SCT/DFT DFT=DFM+DFE 8. Media de cuadrados de los resiudos
- F= MCM/MCE 119. Media de cuadrados totales
- Pvalor_F 3.04265503E-
- R cuadrado ajustado 0. - 𝑆𝐶𝑇=∑▒(𝑌𝑖−𝑌 ̅ )^2 =𝑦𝑖^ cuadrados Total
- ̅ )^2 =𝑦_𝑖^
Xi-X_barra Xi*ui -6 3. -5 7. -4 4. -3 9. -2 2. -1 -14. 0 -10. 1 -21. 2 10. 3 -6. 4 -16. 5 15. 6 1. 0 -13. 14 16 18 20 FRP 4 6 8 10 12 14 16
Cov(ui_gorro,Yi)
Econometría Básica
Docente: Danny Moreno B.
Estimación por Mínimos
Cuadrados Ordinarios MCO
〖𝑌 𝑖 𝑥∑▒𝑖 〗^ 〖𝑋^ _𝑖
∑▒ 〖𝑋 𝑖 𝜇𝑖 〗
Observaciones Yi Xi yi= Xi-X_barra xi=Yi-X_barra yi^2 xi^ 1 4.4567 6 -4.2180076923 -6 17.79158889237 36 2 5.77 7 -2.9047076923 -5 8.437326777751 25 3 5.9787 8 -2.6960076923 -4 7.268457476982 16 4 7.3317 9 -1.3430076923 -3 1.803669661598 9 5 7.3182 10 -1.3565076923 -2 1.84011311929 4 6 6.5844 11 -2.0903076923 -1 4.369386248521 1 7 7.8182 12 -0.8565076923 0 0.733605426982 0 8 7.8351 13 -0.8396076923 1 0.704941076982 1 9 11.0223 14 2.3475923077 2 5.511189643136 4 10 10.6738 15 1.9990923077 3 3.996370054675 9 11 10.8361 16 2.1613923077 4 4.671616707751 16 12 13.615 17 4.9402923077 5 24.40648808544 25 13 13.531 18 4.8562923077 6 23.58357497775 36 Suma 112.7712 156 Media 8.674707692 12 8.759860679 15. Beta2 131.7856 0. 182 Beta1 0 sigma^2 9.695525112 0. 11 var(Beta2) 0.8814113738 0. 182 Varianza muestral 4 -0. 0
1
i_gorro
∑▒𝑌𝑖 ∑▒𝑋𝑖 ∑▒ 〖𝑥 𝑖 𝑦𝑖 〗
(∑▒𝑌𝑖 )/𝑛(∑▒𝑋𝑖^ )/𝑛
(∑▒(𝑌_ 𝑖 𝑌− ̅)^( 2 ∑ ▒)/((𝑋𝑛−1_ 𝑖− )𝑋 ̅)^ 2 )/(𝑛−1)
r^2 9.695525112 0.
var(Beta1) 2054 0. 2366 Pvalor_B1 0 1
Pvalor_B2 0.7240967033 4.96487719E-
Yi_gorro Y_media (Yi_gorro-Ymedia)^ SCE 4.34458022 8.67470769 18.750003928 95. 5.068676923 8.67470769 13. 5.792773626 8.67470769 8. 6.51687033 8.67470769 4. 7.240967033 8.67470769 2. 7.965063736 8.67470769 0. 8.68916044 8.67470769 0. 9.413257143 8.67470769 0. 10.13735385 8.67470769 2. 10.86145055 8.67470769 4. 11.58554725 8.67470769 8. 12.30964396 8.67470769 13. 13.03374066 8.67470769 19. Yi Yi_gorro (Yi-Yi_gorro)^ SCR 4.4567 4.34458022 0. 5.77 5.06867692 0.4918540582 9. 5.9787 5.79277363 0. 7.3317 6.51687033 0. 7.3182 7.24096703 0. 6.5844 7.96506374 1. 7.8182 8.68916044 0. Suma de cuadrados explicada Suma de cuadrado de los residuos
(∑▒𝑋_𝑖^
)/(𝑛∑▒𝑥_
𝑖^2 ) 𝜎^ 2
4
-1.
-0. 0
1
ui_gorro
𝑡=(𝛽 ̂ _1−𝛽_1)/𝑒𝑒(𝛽_1 )
𝑡=(𝛽 ̂ _2−𝛽_2)/𝑒𝑒(𝛽_2 )
𝑆𝐶𝐸=∑▒(𝑌 ̂ _𝑖−𝑌 ̅ )^
𝑆𝐶𝑅=∑▒(𝑌_𝑖−𝑌 ̂ _𝑖 )^2 =𝜇 ̂ _𝑖^
