Lab8_Polynomial Regression

Lab8_Polynomial Regression - EXST 7015 - Statistical...

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EXST 7015 - Statistical Inference II, Fall 2011 Lab 8: Polynomial Regression OBJECTIVES Polynomial regression is a statistical modeling technique to fit the curvilinear data that either shows a maximum or a minimum in the curve, or that could show a max or min if you extrapolated the curve beyond your data. The ability to determine a minimum or maximum point based on the experimental data is a useful application of polynomials. The simple polynomial regressions are multiple regression that use power terms of the independent variable (X i ) with the form of Y= β 0 + β 1 X i + β 2 X i 2 +…+ β k X i k + e i . Notice the subtle difference from multiple linear regression model, here the numbers 2, 3, …,k represent the powers of the same variable. For data that are shaped like a parabola, you probably won't need more than a quadratic model. If the curve trends up again at one end, you'll need a cubic model. Curves with multiple kinks need even higher-order terms. It is obvious that multicollinearity is unavoidable issue in Polynomial regression because the model terms are related to each other. Use of sequentially adjusted type I SS is the solution as presented as the following. Several hypotheses are tested during polynomial regression which is fitted successively starting with the liner term (a first order polynomial). The first null hypothesis, then, is that a quadratic equation does not fit the data significantly better than a linear equation; the next null hypothesis may be that a cubic equation does not fit the data significantly better than a quadratic equation, and so on. Therefore, the sequentially adjusted type I SS should be used when one attempts to test whether a polynomial model is as good as the one with a higher order term. If a particular higher order term is significant, all terms of lower order should be assumed significant and retained in the regression model. There is also a null hypothesis for each equation that says that it does not fit the data significantly better than a horizontal line; in other words, that there is no relationship between the X and Y variables. It should be noticed that the
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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Lab8_Polynomial Regression - EXST 7015 - Statistical...

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