# How to explain the result of this polynomial equation?

Lets say that I predicted plant productivity (logy) by precipitation (logx1) and moisture content of soil (logx2). my original data gives me the best result only after taking logarithm on both side of variables.

mod <- lm(logy ~ poly(logx1*logx2, 2, raw=TRUE)


then I got following coefficients from the model:

intercept=6.773;
logx1*logx2 poly(1) = 2.511;
logx1*logx2 poly(2) = 0.458


With regard to equation, I have 2 questions: 1. How I can explain the result of this equation 2. How to find the value when precipitation is 0.

• How much data do you have? You'd mostly likely do better to have logx1, logx2, their product, their squares, & the product of their squares. (Ie, lm(logy ~ logx1 + logx2 + logx1^2 + logx2^2 + logx1*logx2 + logx1^2*logx2^2).) This is a highly constrained model that is likely to not fit as well. Is there a very well grounded physical theory to justify this version? – gung - Reinstate Monica Jun 24 '19 at 16:37
• Would you please post - or link to - the original non-log data? – James Phillips Jun 24 '19 at 16:47
• @ James Phillips. I am sorry how to add data here? – Sun Rise Jun 24 '19 at 17:19
• You can paste it into the question or link to it. – James Phillips Jun 24 '19 at 18:21
• I have updated above – Sun Rise Jun 24 '19 at 19:12  