Multivariate Regressions

I have temperature data from two different sites, and I want to develop a relationship for temperature between those two sites. In that way, if I have temperature at just one of those sites, I can approximate the temperature at the other site. My question is whether or not a multivariate regression is appropriate here, since each site has the same errors associated with it, and neither site can necessarily be considered the "true" site. So they are both independent variables. Can a multivariate regression be done with only two independent variables, or do I need at least one dependent variable? Is the difference between a multivariate regression and a typical linear regression likely to be significant? And, how would I go about doing a multivariate regression, would I need special software? I'm not terribly familiar with statistical methods, so please dumb down responses as much as possible. Thanks for any help!

Well, as you stated, you would like to use measurements at one site to make a prediction at another. While these two temperatures may indeed be independent, you will be treating one as dependent and the other as independent when you start making predictions. The question here is, which one do you want to use to predict. That is a question that may take more information than what you can get from any type of regression. For example, perhaps one of the sites has more consistent measurements. That is, when it truly is 70 degrees, one is more likely to report that it is 70 degrees.

You dont know which is the best to use as a predictor, so one thing you could do is perfrom two simple linear regressions. In the first, you will use temps from site A as the predictor of temps at site B, and vice versa for the second regression fit. If one of these models has a better fit (Higher R^2), then perhaps this is the model that you should use to predict.

It doesn't make much sense to use a multivariate regression model here since there would be no predictor variables.