the basic setup is as follows: I have a continuous dependent variable (DV, 7 observations) and two continuous independent variables (IV1 & IV2). I would like to evaluate whether adding IV2 as covariate provides added value compared to a regression model with IV1 alone. Normally, one could simply use the Anova function in R to compare both models.
However, the problem is that the observations are not completely independent, and that full correction for all random factors (cf. mixed models approach) is impossible due to the limited setup. Nevertheless, the dependence between the observations is completely captured by IV1, not IV2. E.g. whereas IV1 & DV are heavily correlated (R²~99%), IV2 is not correlated with either IV1 nor DV. FYI: Adding IV2 to the model explains about 95% of the remaining variance, and is significant (p<0.001) when added as independent covariate in the model. Moreover, it results in a reduced RSS for almost all observations.
My question is whether (and why) the p-value for IV2 can (not) be trusted.