Statistical Sciences 1024A/B Lecture Notes - Lecture 9: Dependent And Independent Variables, Scatter Plot
30 Jan 2018
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Regression lines: the (cid:272)orrelatio(cid:374) r (cid:272)a(cid:374) (cid:271)e used to (cid:272)he(cid:272)k (cid:862)dire(cid:272)tio(cid:374)(cid:863), (cid:862)for(cid:373)(cid:863), a(cid:374)d (cid:862)stre(cid:374)gth(cid:863), a regression line: a straight line that describes how a response variable, y changes as an. , (xn; yn): for xi, ^yi = a + bxi fitted (predicted) value of yi, predicted error: ei = yi ^yi , i = 1, 2, . , n: best line: errors e1, e2, . , en are as small as possible: gauss: find a and b such that e2. Residuals of a regression line: those predicted errors e1, e2, . , en in regression line are called residuals: their mean must be zero: (e2 + e2 + . + en) / n = 0: residual plot: it is a scatterplot of (x1, e1), (x2, e2), . , (xn, en): should be as random as possible (no pattern), no up and down pattern, about half position, half negative, can check residuals distribution through histogram.
