# How to analyse data with multiple dependent and independent variables

I have two dependent variables, Abundance and Richness of moths, and 12 independent climate variables. These are Temperature, Rainfall and Sunlight, for each of the 4 seasons.

How do I go about analysing this? From doing individual simple linear regression I have found significance for summer rainfall and winter temperature as factors influencing my dependent variables, but I know that this isn't very statistically viable! Is principle component analysis a suitable way of analysing this data? Are there any other multivariate techniques I could use? Thanks.

• You may want to edit your question to explain that it is a time series. (Same dataset as stats.stackexchange.com/q/87845/32036, right?) This makes the answer somewhat more complex. It's also rather unclear what exactly you're trying to find out. Is it whether your climate variables affect your moth variables in a given season, differently across seasons, etc.? BTW, are abundance and richness continuous, count, or discrete variables? I assume your climate variables are continuous, but this may matter somewhat less...Information about the distributions' shapes would help too. – Nick Stauner Apr 13 '14 at 3:45

Suppose though, that you want to construct a model for both responses simultaneously, and assess the significance of the factors in $that$ model. Then you can use multivariate analysis of covariance (MANCOVA). MANCOVA will provide you with the contribution to the variance in the responses made by each factor, as well as their significance. Note that MANCOVA will produce both type I, II, and III sums of squares (SS). Which one is appropriate depends on the balance of your data. See here for more information on the types of SS. http://mcfromnz.wordpress.com/2011/03/02/anova-type-iiiiii-ss-explained/
#fit a multivariate regression model and then test the type I SS using MANCOVA. fit = lm(formula = cbind(Abundance, Richness) ~ Temp_1 + Rain_1 + Sunlight_1 + Temp_2 + Rain_2 + Sunlight_2 + Temp_3 + Rain_3 + Sunlight_3 + Temp_4 + Rain_4 + Sunlight_4, data = yourData) summary(manova(fit), test="Hotelling-Lawley")  A more thorough overview of how to perform such an analysis is provided here: http://www.uni-kiel.de/psychologie/rexrepos/posts/multRegression.html Note that separate regressions return the same slopes as multivariate regression, and also not that different tests besides the "Hotelling-Lawley" are possible for the MANCOVA test of type I SS, and that you can also test type II SS.