I'm using a multiple linear regression to determine the relationship between certain lifestyle characteristics of a species and the species's tolerance to stress.
The purpose of this analysis is simply to identify factors that may be correlated to differences in tolerance between species and not to predict tolerance (LT50).
Using three lifestyle characteristics (Microhabitat, Tidal Height and Motility) the model is adequate to predict the tolerance of animals (LT50). You can see that each characteristic is a significant model parameter:
lm(formula = LT50 ~ Tidal.Height + Microhabitat + Motility, data = juvdes) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -7.0461 2.7913 -2.524 0.1276 Tidal.Height 5.5866 0.9304 6.004 0.0266 * Microhabitat 10.2704 1.4577 7.046 0.0196 * Motility -6.2125 1.1151 -5.571 0.0307 * Residual standard error: 2.129 on 2 degrees of freedom Multiple R-squared: 0.9884, Adjusted R-squared: 0.971 F-statistic: 56.78 on 3 and 2 DF, p-value: 0.01736
When I add Weight as a variable, all other predictors become non-significant to the model:
lm(formula = LT50 ~ Tidal.Height + Microhabitat + Motility + Weight, data = juvdes) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.4811 24.1076 -0.020 0.987 Tidal.Height 4.7692 3.2240 1.479 0.378 Microhabitat 11.4959 4.8678 2.362 0.255 Motility -7.8169 6.0131 -1.300 0.417 Weight -1580.6541 5731.5419 -0.276 0.829 Residual standard error: 2.903 on 1 degrees of freedom Multiple R-squared: 0.9892, Adjusted R-squared: 0.9461 F-statistic: 22.93 on 4 and 1 DF, p-value: 0.1552
Why does adding weight as a predictors result in all other predictors becoming non-significant? Weight plays a significant role on tolerance (due to SA:V ratio) when comparing tolerance between different ages of a single species, so intuitively it should have some correlation with tolerance when comparing species.