MHB How Do You Calculate the Contribution of Each Element to Total Variance?

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Struggling with a problem dealing with %'s and how to determine the contribution that each element has to the total variance between 2 periods.

Sorry, not sure if there is a way to embed excel spreadsheet into post so included snapshot with my questions/comments.

Rate = Commission / Market

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ValueWhen looking at % change between periods, how do you determine the contribution each element (Commission and Market Value) has to that change?For example, if the Rate (Y) changes from .10% to .15%, what is the contribution of Commission and Market Value to that change?I understand that you can calculate the % contribution for each element to the total variance, but I'm not sure how to do this or if it applies in this situation.Any help would be much appreciated!The best way to approach this problem is to calculate the absolute difference between the two periods for both Commission and Market Value. Then, divide the difference for each element by the total absolute difference for both elements. This will provide you with the percentage contribution of each element to the total change in the rate. For example, if the Commission changed from $20 to $25 and the Market Value changed from $200 to $225, then the absolute difference in Commission is $5 and the absolute difference in Market Value is $25. The total absolute difference is $30. The contribution of Commission to the total change is ($5/$30)*100 = 16.7% and the contribution of Market Value to the total change is ($25/$30)*100 = 83.3%.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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