Explaining variation in a dependent variable based on a factorial experiment I have run a factorial type test in a processing plant and have run a forward and backward step regression in R. 
How can I use the regression results and the anova created from the regression to know what percent of the measured variation of the dependent variable was caused by the purposeful manipulation of the independent variables?
 A: In an anova context, the partial eta squared will tell what % of the Y variance is explained by a given X when controlling for all other X's.  In a regression context, you could refer to the squared partial correlation of the X of interest.  
A: *

*Stepwise regression: I generally would not use stepwise regression to analyse experimental data. Generally you are wanting to test quite specific hypotheses based on the factors that you have manipulated. Also, sample sizes are often smaller in experiments. If you do use stepwise regression, you should at least ensure that you adopt some procedure like cross-validation in order to get an unbiased estimate of your model fit.

*Variance explained: In general as @rolando2 has said partial eta squared describes the percentage of variance explained by a factor, and you could use the overall r-squared to describe the overall variance explained by the model. You may also want to look at omega-squared, because r-squared is biased (i.e., sample values on average are larger than true population values) and omega-squared aims not to be biased.

*Alternative effect size measure: In general, I'm not a big fan of variance explained measures of effect size within the context of experimental manipulation. I prefer unstandardised coefficients or d-based (standardised group mean difference) estimates of effect. This is because the variance explained is contingent on the particular levels that you choose for your experiment. Furthermore, it is often the case that manipulating more factors in a factorial design will reduce the variance explained estimate of each factor. d-based measures often have more meaning across contexts.

