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Regresi linier sederhana

Regresi linier sederhana. Kuliah #2 analisis regresi Usman Bustaman. Apa itu ?. Regresi Linier Sederhana. Regresi ( Buku 5: Kutner , Et All P. 5). Sir Francis Galton (latter part of the 19th century): studied the relation between heights of parents and children

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Regresi linier sederhana

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  1. Regresi linier sederhana Kuliah #2 analisisregresi UsmanBustaman

  2. Apaitu? • Regresi • Linier • Sederhana

  3. Regresi(Buku 5: Kutner, Et All P. 5) • Sir Francis Galton (latter part of the 19th century): • studied the relation between heights of parents and children • noted that the heights of children of both tall and short parents appeared to "revert" or "regress" to the mean of the group. • developed a mathematical description of this regression tendency, • today's regression models (to describe statistical relations between variables).

  4. m B linier • Masihingat Y=mX+B? • Slope? • Konstanta? Y X

  5. Linier lebihlanjut… • Linier dalamparamater… • Persamaan Linier orde 1: • Persamaan Linier orde 2: • Dst… (orde pangkattertinggi yang terdapatpadavariabelbebasnya)

  6. m B sederhana • Relasiantar 2 variabel: • 1 variabelbebas (independent variable) • 1 variabeltakbebas (dependent variable) • Y=mX+B? • Manavariabelbebas? • Manavariabeltakbebas? Y X

  7. Bagaimanamembangun Model Regresi Linier Sederhana?Analisis/Comment Grafik-2 Berikut:

  8. Analisis/Comment Grafik-2 Berikut: B A C D

  9. Fungsi rata-2 (Mean Function) If you know something about X, this knowledge helps you predict something about Y.

  10. Prediksiterbaik… •  Bagaimanamengestimasi parameter dengancaraterbaik…

  11. Regresi Linier

  12. Regresi Linier Populasi Koefisienregresi Sampel ˆ Y = b0 + b1Xi

  13. e = b b + Y X i 0 1 Regresi Linier  Model Y ? (the actual value of Yi) Yi Xi X

  14. Regresiterbaik = minimisasi error • Semua residual harusnol • Minimum Jumlah residual • Minimum jumlahabsolut residual • Minimum versiTshebysheff • Minimum jumlahkuadrat residual  OLS

  15. Ordinary Least Square (OLS)

  16. Assumptions • Linear regression assumes that… • 1. The relationship between X and Y is linear • 2. Y is distributed normally at each value of X • 3. The variance of Y at every value of X is the same (homogeneity of variances) • 4. The observations are independent

  17. Asumsilebihlanjut…Alexander Von Eye & ChristofSchuster (1998) Regression Analysis for Social Sciences

  18. Asumsilebihlanjut…Alexander Von Eye & ChristofSchuster (1998) Regression Analysis for Social Sciences

  19. Proses estimasi parameter (Drapper & Smith)

  20. Koefisienregresi

  21. Simbol-2 (Weisberg p. 22)

  22. Maknakoefisienregresi • b0 ≈ ….. • b1≈ ….. x = 0 ? - Tinggivsberatbadan - Nilai math vs stat - Lama sekolahvspendptn - Lama training vsjmlproduksi …….

  23. A2 B2 C2 yi C y A B SSE Variance around the regression line Additional variability not explained by x—what least squares method aims to minimize SSR Distance from regression line to naïve mean of y Variability due to x (regression) SST Total squared distance of observations from naïve mean of y Total variation B A C yi x Regression Picture

  24. SST (Sum Square TOTAL) Variance to be explained by predictors (SST) Y

  25. SSE & SSR X Variance explained by X (SSR) Y Variance NOT explained by X (SSE)

  26. SST = SSR + SSE Variance to be explained by predictors (SST) X Variance explained by X (SSR) Y Variance NOT explained by X (SSE)

  27. KoefisienDeterminasi Coefficient of Determination to judge the adequacy of the regression model Maknanya: …. ?

  28. KoefisienDeterminasi

  29. Salah pahamttg r2 • R2tinggi prediksisemakinbaik …. • R2 tinggi  model regresicocokdgndatanya … • R2rendah (mendekatinol)  tidakadahubunganantaravariabel X dan Y …

  30. Korelasi Buktikan…! Pearson Correlation…? Correlation measures the strength of the linear association between two variables.

  31. Korelasi & Regresi

  32. Assumptions • Linear regression assumes that… • 1. The relationship between X and Y is linear • 2. Y is distributed normally at each value of X • 3. The variance of Y at every value of X is the same (homogeneity of variances) • 4. The observations are independent

  33. Uji parameter RLS • Linear regression assumes that… • 1. The relationship between X and Y is linear • 2. Y is distributed normally at each value of X • 3. The variance of Y at every value of X is the same (homogeneity of variances) • 4. The observations are independent

  34. Distribusi sampling b1

  35. b1 ~ Normal ~ Normal

  36. Ujikoefisienregresi

  37. Ujikoefisienregresi

  38. SelangKepercayaankoefisienregresi Confidence Interval for b1

  39. Ujikoefisienregresi

  40. SelangKepercayaankoefisienregresi Confidence Interval for the intercept

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