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3

If age and its square are the only predictors, then you should have a coefficient of log-odds on age, call it $b_1$, and one on age squared, call it $b_2$. Hence those are just two terms like those of any quadratic $$b_1 x + b_2 x^2$$ so that a maximum with $x$ will be observed whenever its derivative $b_1 + 2 b_2 x$ is $0$, so long as $b_2 <0$. So the ...

3

In my opinion the 2nd plot is pretty good. I might just add colour = so that each individual has their own colour, but the two main things that jump out about that plot are: there is considerably variation between individuals there is, by comparison, much less variation within individuals there is considerable heterogeneity. In particular, three ...

2

This is essentially the binomial distribution, with $p=0.20$ and $n=|\text{set}|,$ the number of elements in the set.

1

Other options for representing aspects of a distribution are the boxplot and violin plot. Both of these typically represent the median and upper/lower quartile values, showing the range in which the middle 50% of your values fall, and the rest of the plot can give you a sense of the upper/lower range. The violin plot is similar to smoothed histogram or ...

1

So, you know that the true values of this unknown value must be greater than zero? This seems like the perfect time to incorporate a prior. Let's call the random variable $X$. Since we know $X$ cannot be less than zero, you are correct in saying that reporting a value of $X$ as, for example, $X=0.23 \pm 0.44$, does not make much sense. I think in this case, ...

1

With only three years for each occupation, I would start out with visualization. Make a lineplot with 250 lines, years along the x-axis. Plotting ratios directly, that will confound levels with slope, but if there are groups of occupations with rather different slopes, that should stand<out in the plot. You could augment the plot with line coloring ...

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