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I have a dataset which is made up of a binary dependent variable and 3 covariates. My plan was to create a logisitic regression in order to predict the probability of an event happening.

An interesting behavior that I'm seeing is when I plot the individual covariates against the dependent binary variable. I expected a Sigmoid curve to be plotted but instead I'm getting an increasing or decreasing curve which are almost linear. The plots are displayed below. My first thought is these variables have a negative coefficient and therefore to get the Sigmoid curve I'd need to expand the x-axis to include negative values.

The issue I'm having when interpreting this though is that these two variables cannot actually be negative. The first plot covariate is Age and Age cannot be negative. The third plot is a dollar balance and this also cannot be negative.

I'm wondering if my initial interpretation is correct and if it is, how should I proceed knowing that these coefficients are counter-intuitive to what can actually happen, ie age cannot actually be negative.

Covariate1

Covariate2

Covariate3

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    $\begingroup$ If you zoom in on different parts of a sigmoid curve, you can find all of these shapes and more. What's the problem? $\endgroup$
    – Sycorax ♦
    Jan 25, 2021 at 22:25
  • $\begingroup$ The shape of the plots 1 & 3 relative to plot 2 have me confused. I would expect to see, for plot 1, the curve begin at 0 when age is 0 and for plot 3 the curve beginning at 0 when the balance is 0. $\endgroup$
    – user307504
    Jan 26, 2021 at 2:20

1 Answer 1

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An intercept estimates the expected value of the response on the logit scale when all of the features are zero. In this case, the intercept is such that setting all the features to zero yields a prediction that is not zero on the probability scale.

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  • $\begingroup$ Perfect, thank you! $\endgroup$
    – user307504
    Jan 26, 2021 at 12:11

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