Experimental Statistics - week 12.ppt

Chemical Mass Balance 04/26/02 Experimental Statistics - week 12 Begin with all independent variables in the model Find the independent variable that is “least useful” in predicting the dependent variable(i.e. smallest R2, F (or t), etc.) delete this variable if p SLSTAY Continue the process until no further variables are deleted Add independent variables one at a time as in Forward Selection (if p SLENTRY) At each stage perform backward elimination to see whether any variables should be removed (if p SLSTAY) Examine criteria for all acceptable subsets of each “size”, i.e. # of independent variables Criteria: R2, adjusted R2, Cp Note: - transforming Y using the log or square root transformation can help with unequal variance problems - these transformations may also help induce normality hmpg vs hp hmpg vs sqrt(hp) log(hmpg) vs hp log(hmpg) vs log(hp) Chapter 12: Multiple Regression Chapter 13: Variable Selection Model Checking Y X1 X2 4.3 4 .2 5.5 5 .2 6.8 6 .2 8.0 7 .2 4.0 4 .3 5.2 5 .3 6.6 6 .3 7.5 7 .3 2.0 4 .4 4.0 5 .4 5.7 6 .4 6.5 7 .4 Data – Page 628 Y = weight loss (wtloss) X1 = exposure time (exptime) X2 = relative humidity (humidity) Weight loss in a chemical compound as a function of exposure time and humidity The REG Procedure Dependent Variable: wtloss Number of Observations Read 12 Number of Observations Used 12 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr F Model 2 31.12417 15.56208 104.13 .0001 Error