I don't understand this concept well and need help.
I was choosing whether to use a linear model or apply a non-linear transformation in my model formula. To do a diagnostic, I quickly plotted my data:
plotalldaily <- ggplot(amsd, aes(ImpressionsA, Leads.T)) + geom_point(color="orange")+geom_smooth()
From the plot, I guessed that a cubic polynomial transformation of my x variable should give me a better model fit. I referred this: http://www3.nd.edu/~rwilliam/stats2/l61.pdf . On Page 5, there is an explanation of polynomial models with cubic terms.
So I checked the model fit using two formulae- one with the non-linear transformation & another simple linear:
test1 <- lm(Leads.T~ImpressionsA, amsd)
test2 <- lm(Leads.T~I(ImpressionsA^3), amsd)
Strangely, the linear relationship is giving me a better model fit: Lower Standardized Error, Higher R-squared and Better Residuals Distribution.
TEST 1 Residuals
TEST 2 Residuals
I don't know what to make of it. Which model should I fit and what other kind of transformations should I try?