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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
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: