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I assume that you are testing for nonlinearity, not really testing for "linear association". Your results make sense. … Base the pre-specification on if you know from other data that the relationship is linear set knots to zero (linear fit) if you know from other data that the relationship is complex, and especially if …

This goal is inappropriate. Categorization should play no role. Study the continuous relationship between the two continuous variables using a scatterplot and for example the loess nonparametric smo …

In addition to Peter's advice sometimes for count variables a quadratic fit is good, mainly because it is difficult to choose knot locations in a spline function when there are many tied values. As s …

My Regression Modeling Strategies course notes have a detailed example of interpretation for a simple example where age has a linear effect and interacts with sex. …

Although $R^{2} < 0.01$ is not usually very helpful, the value of a model has to also be judged by (1) the difficulty of the task and (2) whether one hopes to learn tendencies vs. predict responses fo …

This is a dangerous data mining procedure that is essentially playing with the data in a way that will badly distort all aspects of statistical inference, starting with a biased (low) estimate of the …

All ordinal regression models in use are nonlinear because they are anchored to a probability scale and regression effects must bend to keep probabilities within [0,1]. You could say that the cumulat …

You are using $R^{2}_{adj}$ incorrectly. It is intended to debias $R^2$ for a single pre-specified model. When used in the context of multiple models the degrees of freedom that needs to be inserted …

With a lot of work you could develop a Bayesian adaptive scheme that allows you to dynamically select test points for each subject based on previous responses. Short of that, the experimental design …

In addition to the excellent answers above, there are general requirements for the linear model to work reasonably well, mainly related to $Y$. … Over many years of experience you'll see that certain variables such as blood pressure tend to behave well in a linear model and others (e.g., blood chemistry measurements) don't. …

When you say bootstrap Monte Carlo I assume you really meant bootstrap. Monte Carlo simulation is for when you know the true underlying (population) model. You did not state what types of model unce …

I say that for several reasons including If you think about the number of non-redundant linear combination of variables that can be analyzed, this number is $\leq \min(n, p)$. …

Linear/nonlinear should not be a binary decision. No magic threshold exists for informing the analyst things like "definitely linear". It's all a matter of degree. … Once you have both linear and flexible fits you can use either log-likelihood or $R^2$ to quantify explained variation in Y. …

Spending time doing ad hoc approaches when logistic regression works just fine is a bit hard to understand. More importantly, your approach breaks down when an estimated probability is 0 or 1 and you …