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
20 Regression Picture C B R2=SSreg/SStotal A2 B2 C2 A y yixy*Least squares estimation gave us the line (β) that minimized C2A B C2SStotalTotal squared distance of observations from naïve mean of y Total variationSSregDistance from regression line to naïve mean of y Variability due to x (regression)SSresidualVariance around the regression line Additional variability not explained by x—what least squares method aims to minimizeR2=SSreg/SStotal