Polynomial example Orthogonal polynomials Statistical power for regression Multiple Regression Week 6 (Wednesday) Lect 6W Constructing polynomial fits Two approaches for constructing polynomial fits Simply create squared, cubed versions of X Center first: Create squared, cubed versions of (X-C) Xc=(X-`X) Xc and Xc2 will have little or no correlation Both approach yield identical fits Centered polynomials are easier to interpret. Lect 6W Example from Cohen Interest in minor subject as a function of credits in minor Lect 6W Interpreting polynomial regression Suppose we have the model Y=b0+b1X1+b2X2+e b1 is interpreted as the effect of X1 when X2 is adjusted Suppose X1=W, X2=W2 What does it mean to "hold constant" X2 in this context? When the zero point is interpretable Linear term is slope at point 0 Quadratic is acceleration at point 0 Cubic is change in acceleration at point 0 Lect 6W Orthogonal Polynomials In experiments, one might have three or four levels of treatment with equal spacing. 0, 1, 2 0, 1, 2, 3 These levels can be used with polynomial models to fit Linear, quadratic or cubic trends We would simply construct squared and cubic forms. Lect 6W Making polynomials orthogonal The linear, quadratic and cubic trends are all going up in the same way. The curve for the quadratic is like the o
