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 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).

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

Linier lebih lanjut… Linier dalam paramater… Persamaan Linier orde 1: Dst… (orde  pangkat tertinggi yang terdapat pada variabel bebasnya)

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

Bagaimana membangun Model Regresi Linier Sederhana Bagaimana membangun Model Regresi Linier Sederhana? Analisis/ Comment Grafik-2 Berikut:

Analisis/Comment Grafik-2 Berikut: D

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

Prediksi terbaik…  Bagaimana mengestimasi parameter dengan cara terbaik…

Regresi Linier

Regresi Linier ˆ Y= 𝛽 0 + 𝛽 1 𝑋 Y = b0 + b1Xi Populasi Koefisien regresi Sampel ˆ Y = b0 + b1Xi

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

Regresi terbaik = minimisasi error Semua residual harus nol Minimum Jumlah residual Minimum jumlah absolut residual Minimum versi Tshebysheff Minimum jumlah kuadrat residual  OLS

Ordinary Least Square (OLS)

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

Asumsi lebih lanjut… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences

Asumsi lebih lanjut… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences

Proses estimasi parameter (Drapper & Smith)

Regression Picture C B R2=SSreg/SStotal A2 B2 C2 A y yi   x y *Least squares estimation gave us the line (β) that minimized C2   A2 B2 C2 SStotal Total squared distance of observations from naïve mean of y  Total variation SSreg Distance from regression line to naïve mean of y  Variability due to x (regression)   SSresidual Variance around the regression line  Additional variability not explained by x—what least squares method aims to minimize R2=SSreg/SStotal