Multiple Regression
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Multiple Regression

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Techniques for Selecting the \"Best\" Regression Equation . The best Regression equation is not necessarily the equation that explains most of the variance in Y (the highest R2).This equation will be the one with all the variables included.The best equation should also be simple and interpretable. (
Multiple Regression

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1. Multiple Regression Selecting the Best Equation

2. Techniques for Selecting the "Best" Regression Equation The best Regression equation is not necessarily the equation that explains most of the variance in Y (the highest R2). This equation will be the one with all the variables included. The best equation should also be simple and interpretable. (i.e. contain a small no. of variables). Simple (interpretable) & Reliable - opposing criteria. The best equation is a compromise between these two.

3. We will discuss several strategies for selecting the best equation: ? All Possible Regressions Uses R2, s2, Mallows Cp ? Cp = RSSp/s2complete - [n-2(p+1)] "Best Subset" Regression Uses R2,Ra2, Mallows Cp Backward Elimination Stepwise Regression

4. An Example In this example the following four chemicals are measured: X1 = amount of tricalcium aluminate, 3 CaO - Al2O3 X2 = amount of tricalcium silicate, 3 CaO - SiO2 X3 = amount of tetracalcium alumino ferrite, 4 CaO - Al2O3 - Fe2O3 X4 = amount of dicalcium silicate, 2 CaO - SiO2 Y = heat evolved in calories per gram of cement.

5. The data is given below:


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