Allright, I'm having a bit of trouble with something.

I have two sets of numbers, one is an attempt to predict the other.
To be specific, one is an attempt to compute changes in the USD/AUD exchange rate with data from 3 months before, one is what the change in the exchange rate is after three months actually was. (this was done with historical data).

Now it's been a while since I did regression modeling(I know this isn't least squares regression:P), but I believe that the mean sum of squares is the sum of the squared predicted values, while the sum of squared error is the sum of the difference between the predicted values and the actual values.

I *think* that's right.

My big question is on how I can perform an F test. To test the significance. I've been looking, but I can't seem to work out how to use the formula for this case. (the SSE of the null hypothesis?)
Most of my experience with this sort of stuff has been fitting linear models in SPLUS, not testing dodgy theoretical models.

Surely someone here is good at statistics

Statistics show I suck with all forms of statistics. Tricky ain't it?

Use it on the lottery and forward the results to me.

Linear regression is precisely what you would use, and it is least squares since you're relating two variables. The only reason why you should be using an F test is in an ANOVA to test the significance of the model slope, where your null hypothesis is basically "no regression model exists."

What I'm worried about though is this data. You only use regression analysis when the error (what isn't predicted by your model) is normally distributed, so the dependent variable is explained to a good extent by the predictor(s). What it doesn't account for is any "internal structure" of the variables, like seasonal variation. That's why linear regression doesn't sound to me like an appropriate treatment for the differences in exchange rates over 3 months. If that's the case you have to use (much) more complicated methods from time series forecasting like ARMA.

Post the data and I can try to give you better advice, but my specialty is categorical data analysis so I'm not sure how much I can help. If this is for a class assignment your professor probably just wants to make sure you know regression procedures, not necessarily have suitable data.