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Percent Contribution How-To

This walkthrough uses a small model you can build in a minute: two inputs, one output, and a specification band that half the output sits outside of.

Press Copy for Excel, then paste the table into a blank worksheet.

Model Value
Wall thickness 10
Bore 4
Outside width =B2*2+B3

Click cell A1 in a blank worksheet and press Ctrl+V. The two headings land in row 1, the labels in column A, and the model in column B: B2 holds the wall thickness, B3 the bore, and B5 the formula that reads them both. The empty row is deliberate, so the output lands in B5 and not B4, which is what every Monte Carlo walkthrough calls it.

Mark B2 and B3 as inputs with Mark Input, giving each a Normal distribution: B2 mean 10 standard deviation 0.2, B3 mean 4 standard deviation 0.1. Mark B5 as an output with Mark Output and give it a lower limit of 23 and an upper limit of 25.

Steps

  1. Run the model first. Percent Contribution reads trials, so Run Model has to have run.

  2. QXL Monte Carlo New > Monte Carlo > Contribution Tools > Percent Contribution...

  3. Leave the method at its default and press the button that runs it.

What you should see, and why

B2 should take much the larger share. The model is B5 = B2*2 + B3, so B2 enters with a coefficient of 2 and B3 with 1. Contribution goes with the coefficient and the input's own spread together, and here B2 has both the larger coefficient and the larger standard deviation.

Work it out before you look. B2 contributes about (2 * 0.2)^2 = 0.16 and B3 about (1 * 0.1)^2 = 0.01, so B2 should hold roughly 94 percent of the variance and B3 roughly 6 percent. A result far from that means the model or the markings are not what you think.

Unexplained Variation should be almost nothing. The model is a weighted sum of the inputs, which is exactly what a linear decomposition reproduces, so R-squared should be close to 1.

Now make the unexplained part appear

Change B5 to =B2*B3 and run the model and the contribution again.

Unexplained Variation is now clearly nonzero, because a product is not a weighted sum and a straight line cannot reproduce it. That bar is the honest statement that the linear decomposition does not account for everything, and it is the reason to read it rather than ignore it.

Things to try next

  • Switch the method to LMG and compare. Its shares are non-negative and sum to R-squared by construction, which the Type III shares do not.
  • Make the two inputs correlated and look at Shared Variation under Type III. It grows with the correlation, and Math Details explains why neither input is credited with it.
  • Give B3 a standard deviation of 1 and watch the shares swap over.

See Also