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Multiple Linear Regression

Multiple Linear Regression. (MLR). Three General Techniques for Model Building. Three General Techniques for Model Building. All possible regressions. Forward selection. Backward elimination. With k = 2 independent variables there are four possible regression models:. 1) 2) 3) 4).

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Multiple Linear Regression

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  1. Multiple Linear Regression (MLR) Three General Techniques for Model Building

  2. Three General Techniques for Model Building • All possible regressions. • Forward selection. • Backward elimination.

  3. With k = 2 independent variables there are four possible regression models: 1) 2) 3) 4) Three General Techniques for Model Building • All possible regressions. Note that the net regression coefficients differ from one model to another. Neither independent variable is related to the yi.

  4. Three General Techniques for Model Building • All possible regressions. With k = 6 independent variables how many possible regression models are there?

  5. Three General Techniques for Model Building • All possible regressions. • Forward selection. • Backward elimination.

  6. Three General Techniques for Model Building • Forward selection. This technique works in phases. Phase 1: Solve every possible regression model using one independent variable. } For example, assume that the model using x3 is the best. y, x1 y, x2 y, x3 y, x4 y, x5 y, x6 Pick the best solution (i.e. the one with the largest R Square). Now, proceed to Phase 2.

  7. Three General Techniques for Model Building • Forward selection. Phase 2: Solve every possible regression model using two independent variables (that use the best set from the previous phase). } For example, assume that the model using x3 and x5 is the best. y, x3, x1 y, x3, x2 y, x3, x4 y, x3, x5 y, x3, x6 Pick the best solution (i.e. the one with the largest R Square). Now, proceed to Phase 3. . . .

  8. Three General Techniques for Model Building • Forward selection. Phase 3: Solve every possible regression model using three independent variables (that use the best set from the previous phase). QUESTION: When do you STOP this process? (i.e. When do you know that you have found a good MIX of independent variables?) ANSWER: by testing the additional contribution of each new independent variable

  9. Three General Techniques for Model Building • All possible regressions. • Forward selection. • Backward elimination. Begin with all the independent variables and eliminate them, one at a time, until you find a good MIX of independent variables.

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