POL232H1 Lecture Notes - Lecture 6: Multivariate Analysis, Regression Analysis
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Compute the conditional means of y given each value of x. How y would vary on average as x changes (simple) linear regression: use a straight line to model the conditional means of y given x. Conditioned means of y given x are modeled as. We may use any symbol as long as we properly define them. Conditional means of y are modeled as. ^y = values of y along the linear regression line (predicted or fitted values) B0 = value of y when x =0. B* = change in ^y with respect to one unit change in x. B* represents how y would vary, on average, as x changes by one unit. Suppose that there is a positive causal relationship between x and y. Confounding variable: z is a confounding variable if it has a relationship both with x and y. Omitted variable bias: if we omit z, b* = b + (y x a)
