# Model from $\hat{Y}$s or model from residuals?

This is for modeling revenue by looking at historical data.

I am trying to estimate a curve where x = Fiscal Year Quarter and Y = % of Revenue for lifetime of a bid(sale/opportunity/whatever term makes the most sense to you...)

The goal of this is so when a sales person puts in a bid that says "This is worth 50,000 over 3 years", we can then use a rough estimate for about how much % of that 50k we will see each quarter over the next 12 quarters (3x4=12).

Now there are 5 different time spans that fit 90% of our sales that is 1/2/3/4/5 years. There are also 4 different market types we sell to. Currently I have been breaking down each market into 5 models, one model for each year and using Polynomial Linear Regression. Granted the R^2 isn't the best but it is the best we can hope for.

In the end I need to take the models from all 4 markets and make a single model that can be applied to all sales overall. That way we have 5 models not 20 (4x5=20) models. My question is when I have all of the models from each market should I take all of the 1 year models and extract the Yhats from the models, plot those then make a model off those? Or should I take all of the 1 year models extract the residuals and make a model off those? Then do the same for the 2/3/4/5 year models to end up with 5 models, or is there a far better way to model this that someone might point me in the direction of?

Thank you for any help or collaborative thinking in advance.

Edit 1

Example :

Sorry for not labeling the Axis on the graph but the X is Quarters. So 1 is the first Quarter Revenue from that Market. Y is Percent of Revenue of Lifetime Revenue, so when (1,1) For the BlueLine = then that Market is expected to generate about 1% of the lifetime revenue that item is estimated to make.

Here are 3 of the Market's for a 5 year run (Each model is made out of different data as things sold as "Market 1" can't be sold as "Market 2". The Fiscal Quarter they come from vary as "Market 1" doesn't sell at the same time as "Market 2". I need to figure out a single model that can as best as I can estimate how a 5 year (20 quarter) would look no matter the market. That way I could take a bid for X dollars over 20 quarters no matter the market and estimate my revenue projections off a single model.

Hopefully this is a bit easier to follow. I would have originally posted these graphs but I was still in the process of finding the base models.

So would I do as I did below the 3 lines and model just off the $\hat{Y}$s or would I do as offered by @Glen_b and model off both the Residuals and the $\hat{Y}$s?

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While I'm not totally clear on what you're doing, I'd be inclined to combine the data (keeping track of which time span they're from, as it may be relevant in modelling the combined data) rather than the fits. If your data are not from separate time periods there will probably be dependence issues that should be included as part of the modelling (and since they're time series there may also be autocorrelation or even series integration/cointegration issues). If you do calculate yhats you should estimate their variances (since the yhats won't be equally precise) before trying to model them. –  Glen_b Oct 25 '12 at 6:27