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REGRESI LINIER SEDERHANA KULIAH #2 ANALISIS REGRESI Usman Bustaman 1.

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Presentasi berjudul: "REGRESI LINIER SEDERHANA KULIAH #2 ANALISIS REGRESI Usman Bustaman 1."— Transcript presentasi:

1 REGRESI LINIER SEDERHANA KULIAH #2 ANALISIS REGRESI Usman Bustaman 1

2 APA ITU? Regresi Linier Sederhana 2

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). 3

4 LINIER Masih ingat Y=mX+B? Slope? Konstanta? B m X Y 4

5 LINIER LEBIH LANJUT… -Linier dalam paramater… -Persamaan Linier orde 1: -Persamaan Linier orde 2: -Dst… (orde  pangkat tertinggi yang terdapat pada variabel bebasnya) 5

6 SEDERHANA Relasi antar 2 variabel: 1 variabel bebas (independent variable) 1 variabel tak bebas (dependent variable) Y=mX+B? Mana variabel bebas? Mana variabel tak bebas? B m X Y 6

7 BAGAIMANA MEMBANGUN MODEL REGRESI LINIER SEDERHANA? Analisis/ Comment Grafik-2 Berikut: 7

8 Analisis/Comment Grafik-2 Berikut: A B CD 8

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

10 PREDIKSI TERBAIK…  Bagaimana mengestimasi parameter dengan cara terbaik… 10

11 Regresi Linier 11

12 Regresi Linier Koefisien regresi Populasi Sampel ˆ Y = b 0 + b 1 X i 12

13 Regresi Linier  Model i  X Y YX    YiYi XiXi ? (the actual value of Y i ) 13

14 REGRESI TERBAIK = MINIMISASI ERROR -Semua residual harus nol -Minimum Jumlah residual -Minimum jumlah absolut residual -Minimum versi Tshebysheff -Minimum jumlah kuadrat residual  OLS 14

15 ORDINARY LEAST SQUARE (OLS) 15

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 16

17 ASUMSI LEBIH LANJUT… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences 17

18 ASUMSI LEBIH LANJUT… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences 18

19 PROSES ESTIMASI PARAMETER (Drapper & Smith) 19

20 KOEFISIEN REGRESI 20

21 SIMBOL-2 (Weisberg p. 22) 21

22 MAKNA KOEFISIEN REGRESI b 0 ≈ ….. b 1 ≈ ….. ? x = 0 - Tinggi vs berat badan - Nilai math vs stat - Lama sekolah vs pendptn - Lama training vs jml produksi ……. 22

23 C A B A yi yi x y yi yi C B A 2 B 2 C 2 SST Total squared distance of observations from naïve mean of y Total variation SSR Distance from regression line to naïve mean of y Variability due to x (regression) SSE Variance around the regression line Additional variability not explained by x—what least squares method aims to minimize REGRESSION PICTURE 23

24 Y Variance to be explained by predictors (SST) SST (SUM SQUARE TOTAL) 24

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

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

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

28 Koefisien Determinasi 28

29 SALAH PAHAM TTG R 2 1.R 2 tinggi  prediksi semakin baik …. 2.R 2 tinggi  model regresi cocok dgn datanya … 3.R 2 rendah (mendekati nol)  tidak ada hubungan antara variabel X dan Y … 29

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

31 KORELASI & REGRESI 31

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 32

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 33

34 DISTRIBUSI SAMPLING B1 34

35 35

36 Uji koefisien regresi 36

37 Uji koefisien regresi 37

38 Selang Kepercayaan koefisien regresi Confidence Interval for   38

39 Uji koefisien regresi 39

40 Confidence Interval for the intercept Selang Kepercayaan koefisien regresi 40


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