Regresi linier sederhana

Presentasi berjudul: "Regresi linier sederhana"— Transcript presentasi:

1 Regresi linier sederhana
Kuliah #2 analisis regresi Usman Bustaman @akbardarmawan/3SE1

2 Apa itu? Regresi Linier Sederhana @akbardarmawan/3SE1

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). @akbardarmawan/3SE1

4 linier Masih ingat Y=mX+B? Slope? Konstanta? m B Y X
@akbardarmawan/3SE1

5 Linier lebih lanjut… Linier dalam paramater… Persamaan Linier orde 1:
Dst… (orde  pangkat tertinggi yang terdapat pada variabel bebasnya) @akbardarmawan/3SE1

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? Y m X B @akbardarmawan/3SE1

7 Bagaimana membangun Model Regresi Linier Sederhana
Bagaimana membangun Model Regresi Linier Sederhana? Analisis/ Comment Grafik-2 Berikut: @akbardarmawan/3SE1

8 Analisis/Comment Grafik-2 Berikut:
D @akbardarmawan/3SE1

9 Fungsi rata-2 (Mean Function)
If you know something about X, this knowledge helps you predict something about Y. @akbardarmawan/3SE1

10 Prediksi terbaik…  Bagaimana mengestimasi parameter dengan cara terbaik… @akbardarmawan/3SE1

11 Regresi Linier @akbardarmawan/3SE1

12 Regresi Linier ˆ Y= 𝛽 0 + 𝛽 1 𝑋 Y = b0 + b1Xi Populasi
Koefisien regresi Sampel ˆ Y = b0 + b1Xi @akbardarmawan/3SE1

13 Regresi Linier  Model Y X b b + = e Y X Yi Xi
? (the actual value of Yi) Y X b b + = Yi i e Xi X @akbardarmawan/3SE1

14 Regresi terbaik = minimisasi error
Semua residual harus nol Minimum Jumlah residual Minimum jumlah absolut residual Minimum versi Tshebysheff Minimum jumlah kuadrat residual  OLS @akbardarmawan/3SE1

15 Ordinary Least Square (OLS)
@akbardarmawan/3SE1

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 @akbardarmawan/3SE1

17 Asumsi lebih lanjut… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences @akbardarmawan/3SE1

18 Asumsi lebih lanjut… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences @akbardarmawan/3SE1

19 Proses estimasi parameter (Drapper & Smith)
@akbardarmawan/3SE1

20 Koefisien regresi @akbardarmawan/3SE1

21 Simbol-2 (Weisberg p. 22) @akbardarmawan/3SE1

22 Makna koefisien regresi
x = 0 ? b0 ≈ ….. b1 ≈ ….. - Tinggi vs berat badan - Nilai math vs stat - Lama sekolah vs pendptn - Lama training vs jml produksi ……. @akbardarmawan/3SE1

23 Regression Picture C B SSE SSR Variability due to x (regression)
yi x y A B C2 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 @akbardarmawan/3SE1

24 explained by predictors
SST (Sum Square TOTAL) Variance to be explained by predictors (SST) Y @akbardarmawan/3SE1

25 SSE & SSR (SSR) (SSE) X Y Variance explained by X Variance NOT
@akbardarmawan/3SE1

26 explained by predictors
SST = SSR + SSE Variance to be explained by predictors (SST) X Variance explained by X (SSR) Y Variance NOT explained by X (SSE) @akbardarmawan/3SE1

27 Coefficient of Determination
Koefisien Determinasi Coefficient of Determination to judge the adequacy of the regression model Maknanya: …. ? @akbardarmawan/3SE1

28 Koefisien Determinasi
@akbardarmawan/3SE1

29 Salah paham ttg r2 R2 tinggi  prediksi semakin baik ….
R2 tinggi  model regresi cocok dgn datanya … R2 rendah (mendekati nol)  tidak ada hubungan antara variabel X dan Y … @akbardarmawan/3SE1

30 measures the strength of the linear association between two variables.
Korelasi Buktikan…! Pearson Correlation…? Correlation measures the strength of the linear association between two variables. @akbardarmawan/3SE1

31 Korelasi & Regresi 𝑺 𝒀 = 𝑺 𝒀𝒀 𝑺 𝑿 = 𝑺 𝑿𝑿 @akbardarmawan/3SE1

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 @akbardarmawan/3SE1

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 @akbardarmawan/3SE1

34 Distribusi sampling b1 @akbardarmawan/3SE1

35 b1 ~ Normal  ~ Normal @akbardarmawan/3SE1

36 Uji koefisien regresi @akbardarmawan/3SE1

37 Uji koefisien regresi @akbardarmawan/3SE1

38 Confidence Interval for b1
Selang Kepercayaan koefisien regresi Confidence Interval for b1 @akbardarmawan/3SE1

39 Uji koefisien regresi @akbardarmawan/3SE1

40 Confidence Interval for the intercept
Selang Kepercayaan koefisien regresi Confidence Interval for the intercept @akbardarmawan/3SE1