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My problem is very simple and I have searched the web to my best capabilities but still haven't found any solutions to my problem, and sadly I have no one to ask in real life. Anyway, my problem is stated as follows: I have no idea if my logistic regression is reasonable/ correct.

I analyze horse racing as a hobby and have read about logistic regression in pretty much every paper I have read, so I thought I'd give it a shot. I get the basics of it: A linear regression is not suitable for classification problems since a linear regression will take values above 1 and below 0, this is not okay in the world of probabilities! Hence, logistic regression fixes this issue.

I've scatter plotted my variables and fitted a line to it, which is on the form y = B0+X1*B1, where X1 is my independent variable (in this case the sortPriority/ postPosition of the horse). I know that the formula for linear regression is on the form p = 1/(1+e^(-y)). The scatter looks like this: ![See the issue Blue is linear regression, orange "is" logistic regression and the green marks are my data points. The code I used is as follows:

m, b = np.polyfit(sortedDataframe[stuffToEstimate],Binary_runnerResult,1) plt.scatter(sortedDataframe[stuffToEstimate],Binary_runnerResult,marker='+', color = 'green') Where m is the intercept and b is the slope of the fitted line.

plt.plot(np.linspace(0,500,1000),[b+m*i for i in np.linspace(0,500,1000)]) plt.plot(np.linspace(0,500,1000),[1/(1+np.e**(-(b+m*i))) for i in np.linspace(0,500,1000)])

Now, this might be a stupid question, but does this even look somewhat reasonable/ correct? In all the tutorials I've watched they all get this really nice S-shape, which makes sense because their datasets "looks cleaner" than mine. This might be because the nature of horse racing is very different from calculating if you'll get a mortgage based on credit score, i.e. people with low credit score almost never get a mortgage and people with high credit score almost always get a mortgage whereas a horse with low sortPriority doesn't almost always win a race. Though I feel that I should have a stronger S-shape then I have since sortPriorities 5-15 never won a race. I also have this plot where the issue might not be as obvious: Not so obvious issue? I'm not sure..

So back to my question: How would I make this better?

I realize that I cant do a logistic regression on all my data all at once, the regressions in the plot for example are from races on 2000m distance and on a specific class. But I'm afraid that I will overfit my model if I add more restrictions on the dataset.

Last question: Is it even correct to pick a dataset that contains all of the horses of a race or should I maybe pick individual horses that fit what I want to regress?

Sorry for the wall of text but any help would be much appreciated. Cheers!

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    $\begingroup$ "The scatter looks like this: See the issue?"—There's no image! $\endgroup$ Jun 29, 2021 at 20:32
  • $\begingroup$ Im so sorry! I copy/ pasted it from Stack Overflow and completely forgot about the pictures. I have now added the pictures along with some details. Cheers! $\endgroup$ Jun 30, 2021 at 7:47

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One tool that may help part of checking a logistic model, at least in R, is the DHARMa package. It runs linear and, at minimum, binomial generalised linear model simulations. Check its details on CRAN. It outputs qqplot normality, dispersion and outlier tests and a fitted vs. predicted residual error plot with warnings. As for which predictors to use from the data, a clear research question may help to inform where to start in the data modelling.

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  • $\begingroup$ Thanks for the response! I haven't used R as og yet but I will check it out anyway! I've found several packages to aid me but I'd really like to learn how to do it on my own first, otherwise I wont understand how to use the packages properly. $\endgroup$ Jun 30, 2021 at 7:50
  • $\begingroup$ DHARMa looks very interesting. The package includes a reference manual, but this only lists the functions. Are you aware of an introductory article explaining its methods and its use? $\endgroup$
    – cdalitz
    Jun 30, 2021 at 14:21

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