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REGRESI LINIER SEDERHANA KULIAH #2-5 ANALISIS REGRESI Usman Bustaman.

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Presentasi berjudul: "REGRESI LINIER SEDERHANA KULIAH #2-5 ANALISIS REGRESI Usman Bustaman."— Transcript presentasi:

1 REGRESI LINIER SEDERHANA KULIAH #2-5 ANALISIS REGRESI Usman Bustaman

2 APA ITU? 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 LINIER Masih ingat Y=mX+B? Slope? Konstanta? B m X Y

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

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

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

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

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

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

11 Regresi Linier

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

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

14 REGRESI TERBAIK = MINIMISASI ERROR -Semua residual harus nol -Minimum Jumlah residual -Minimum jumlah absolut residual -Minimum versi Tshebysheff -Minimum jumlah kuadrat 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 ASUMSI LEBIH LANJUT… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences

18

19 PROSES ESTIMASI PARAMETER (Drapper & Smith)

20 KOEFISIEN REGRESI

21 SIMBOL-2 (Weisberg p. 22)

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 …….

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

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

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

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

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

28 Koefisien Determinasi

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 …

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

31 KORELASI & REGRESI

32 UJI PARAMETER RLS Kuliah 4

33 QUIZZZ…. 1.Tuliskan pengertian anda mengenai Teorema Limit Pusat (Central Limit Theorem -- CLT) dan apa manfaatnya! 2.Tuliskan statistik uji yang tepat dan asumsi yang digunakan untuk uji hipotesis berikut: H 0 : µ = 0 vs H 1 : µ ≠ 0 3.Tuliskan statistik uji yang tepat dan asumsi yang digunakan untuk uji hipotesis berikut: H 0 : µ 1 = µ 2 = µ 3 = µ 4 vs H 1 : setidaknya ada 1 µ i = µ j, i ≠ j

34 REVIEW CLT Manfaat ?  Penentuan jml sampel (n)  Uji Hipotesis

35 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

36 UJI SIGNIFIKANSI PARAMETER β 1 Apa artinya?

37 DISTRIBUSI SAMPLING B1

38 H 0 : µ = 0 H 1 : µ ≠ 0 ≈

39 Uji koefisien regresi

40

41 Selang Kepercayaan koefisien regresi Confidence Interval for  

42 Uji koefisien regresi

43 Confidence Interval for the intercept Selang Kepercayaan koefisien regresi

44 PREDIKSI

45 SELANG KEPERCAYAAN UNTUK E(Y)

46 UJI RATA-2 > 2 POPULASI H 0 : µ 1 = µ 2 = µ 3 = µ 4 H 1 : setidaknya ada 1 µ i = µ j, i ≠ j  ANOVA (Analysis of Variance) Asumsi :

47 ANOVA Statistik Uji: Variasi Antar Sampel (Between Sample Variation) Variasi Intra Sampel (Within Sample Variation)

48


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