SOC202H1 Lecture Notes - Lecture 10: Directional Statistics, Stellar Population, General Linear Model
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Linear regression: a linear equation is the tool for formally expressing the relationship in a scatterplot, this simple equation is known as the regression line. Deterministic relationship: all observations fall perfectly along the straight line. Absent a determinist relationship, we must choose a line that minimizes the squared distances of all o(cid:271)se(cid:396)vatio(cid:374)s" poi(cid:374)ts to the li(cid:374)e the least squares regression line. Note that the solid line provides a better fit to the data than the dashed line, even though the dashed line fits two data points exactly. The least squares line reduces the amount of squared error: Returning to the example of how prior convictions are associated with sentence length: (cid:895) Y h t g (cid:374) e l e (cid:272) (cid:374) e t (cid:374) e. Y = a + (b)x is the e(cid:395)uatio(cid:374) that (cid:396)ep(cid:396)ese(cid:374)ts this (cid:396)eg(cid:396)essio(cid:374) li(cid:374)e. let"s (cid:272)al(cid:272)ulate the values fo(cid:396) a (intercept) and b (slope).
