From forecasting the onset of the Monsoon in India, to mapping the drought in the USA, and worsening
drought in Australia, insight from statistics into rainfall patterns affects everyone. The following documents contain technical information on regression models and rainfall, organized from the simplest linear regression to the more technical local spatial and temporal fitting techniques.
Statistics 301 Handout #30: Simple Linear Regression contains R code with simple regression exercises.
Partial Correlation Coefficients by Gerard E. Dallal, Ph.D. provides some climatic related examples of scatterplots and partial correlation coefficients.
More advanced approaches to reconstruction of rainfall fields use a form of local regression. Here a partial thin plate smoothing spline is used for SPATIAL MODELLING OF CLIMATIC VARIABLES ON A CONTINENTAL SCALE
Here is another good example where local fitting techniques have been used for Estimation of Precipitation by Kriging in the EOF Space of theSea Level Pressure Field.
Some of the most advanced and insighful work on rainfall modeling is by Koutsoyiannis, e.g. An entropic-stochastic representation of rainfall intermittency: The origin of clustering and persistence, Water Resources Research, 42(1), W01401, 2006.
Here is the technical documentation of software SPLINA and SPLINB.
The additive regression model appears to be a practical option for analysing spatially varying effects of several predictors on observed phenomena. It is attractive from the point of view of overcoming curse of dimension problems associated with the analysis of noisy multivariate data. Moreover its implementation is a straightforward extension of standard thin plate spline
Splines are a standard technique well defined by statisticians and appear to be suitable for reconstruction of past climates from proxy records. Yet climate scientists associated with Michael Mann continue to develop ad hoc methodologies with questionable assumptions without the benefit of statisticians as criticised in the Wegman report. The lesson for successful prediction is like the old saw: brain surgery is not for do it yourselfers.