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 childrennoted 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).
16 Assumptions Linear regression assumes that… 1. The relationship between X and Y is linear2. Y is distributed normally at each value of X3. 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 Asumsi lebih lanjut… Alexander Von Eye & Christof Schuster (1998) Regression Analysis for Social Sciences
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…….
23 Regression Picture C B SSE SSR Variability due to x (regression) yixyA B C2SSTTotal squared distance of observations from naïve mean of y Total variationSSRDistance from regression line to naïve mean of y Variability due to x (regression)SSEVariance around the regression line Additional variability not explained by x—what least squares method aims to minimize
24 explained by predictors SST (Sum Square TOTAL)Variance to beexplained by predictors(SST)Y
25 SSE & SSR (SSR) (SSE) X Y Variance explained by X Variance NOT
26 explained by predictors SST = SSR + SSEVariance to beexplained by predictors(SST)XVariance explained by X(SSR)YVariance NOTexplained by X(SSE)
27 Coefficient of Determination Koefisien DeterminasiCoefficient of Determinationto judge the adequacy of the regression modelMaknanya: …. ?
33 QUIZZZ….Tuliskan pengertian anda mengenai Teorema Limit Pusat (Central Limit Theorem -- CLT) dan apa manfaatnya!Tuliskan statistik uji yang tepat dan asumsi yang digunakan untuk uji hipotesis berikut:H0: µ = 0 vs H1: µ ≠ 0H0: µ1 = µ2 = µ3 = µ4 vs H1: setidaknya ada 1 µi = µj , i ≠ j
35 Uji parameter RLS Linear regression assumes that… 1. The relationship between X and Y is linear2. Y is distributed normally at each value of X3. The variance of Y at every value of X is the same (homogeneity of variances)4. The observations are independent