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It is very difficult to achieve what you want programmatically because there are so many different forms of nonlinear associations. Even looking at correlation or regression coefficients will not really help. It is always good to refer back to Anscombe's quartet when thinking about problems like this: Obviously the association between the two variables is ...


5

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. Instead, consider quantifying the degree of linearity. This can be measured relative to explained variation in Y be two competing models: one that forces linearity and one that doesn'...


4

Simple example: R code is not as elegant as it might be, but I hope transparent. set.seed(2020) n = c(5, 10, 20, 5, 7, 15) x1 = rpois(5, 5); x2 = rpois(10, 3) x3 = rpois(20, 1); x4 = rpois(5, 7) x5 = rpois(7, 3); x6 = rpois(15, 2) a = c(mean(x1), mean(x2), mean(x3), mean(x4), mean(x5), mean(x6)) x = c(x1, x2, x3, x4, x5, x6); m = rep(1:6, n) boxplot(x~...


4

A classical solution is to apply a robust local smoother. In his book EDA (Addison-Wesley 1977), John Tukey lays out principles and procedures based primarily on running local medians. When a median of an odd number $2k+1$ of data is computed, up to $k$ of those values may be extreme yet the median will be finite and well-defined. Handling infinities is ...


3

The biggest problem you have here is that "non-linear relation" is not well defined. If you allow for any non-linear relation, there's basically no way to tell if something is "completely random" or just follows a non-linear relation that looks exactly like something that might come out of a "completely random" set up. However, ...


2

tldr: Denser implies steeper gradient. On a contour plot, the value on the continuous plot is the same. What might be helpful in your plot is to give numbers to the contour lines. Imagine a Z-axis, rising out of the screen. If we plot, $z^2 = x^2 + y^2$, For a circle with radius 1, the circle will be created a unit distance out of the screen. For radius, 2 ...


2

Vertical values are described by the y-axis title and tick labels: Daily % of Delayed Flights. So the masses Alaska, Delta, and JetBlue indicate that for some portion of the days measured, those three airlines had no delayed flights (i.e. had 0% of flights delayed). The width describes $2$ $\times$ the probability density, but also $2$ $\times$ the (...


2

Your favourite statistical software, or software you use to do statistics, should be programmable, and if not you need a new favourite. That means not being obliged to reach for a standard plot, or an existing routine, but being able to customise a display according to what you want. Here I thought up a plot showing all the data, a box with whiskers to the ...


2

I know this as an empirical survival plot for the corresponding variable, grouped by another factor. Note that the values plotted are simply $1 - \hat{F_n}(i)$ where $\hat{F_n}(\cdot)$ is the empirical cumulative distribution function.


1

t-SNE pairwise selects all the distances in the high-dimensional space and tries to preserve these in a lower-dimensional space. For a given point it calculates the distance from all other points in high-dimensional space, and gives each of these a probability (close points have a higher probability). It then does the same for all other points, and ...


1

In qualitative methods, this 'point' is termed "data saturation". This is conventionally defined as the point when “no new information or themes are observed in the data” (Guest, Bunce, & Johnson, 2006, p. 59). Personally I see no reason why this term (and the general concept) cannot also be used with quantitative methods as well. Reference: ...


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