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Is this null hypothesis TESTABLE?

  • Research Question: "Can a predictive model utilizing logistic regression be built which predicts at least one customer will churn in 90 days, and this individual prediction will be at a minimum of 70% confidence, using a chosen set of independent variables?"
  • Null Hypothesis: "A predictive model utilizing logistic regression cannot predicts at least one customer will churn in 90 days, with this individual prediction being at a minimum of 70% confidence, using a chosen set of independent variables."

If so, how do you test the "70% confidence" of the particular churn event that allows you to reject the null hypothesis, at the p < 0.05 level? I'm not sure the confidence of an individual prediction can be done, but that may depend on the modeling technique. It may be that you drop the p < 0.05, and just use the validity of the full model (R-square and Pearson chi-square with logistic regression).

Or, is this the only way to write the null hypothesis, and the strength of the model must be left to the discussion section?

  • "There is no significant relationship between the full model using the chosen independent variables and customer churn." (With r-square and chi-square showing the significance of the full model.)
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  • $\begingroup$ Voted close for being off topic. $\endgroup$
    – Ethan
    Aug 6, 2019 at 20:33
  • $\begingroup$ Ethan, You think this has nothing to do with Data Science? My post is about predictive analytics, logistic regression, and statistical significance. $\endgroup$
    – user79134
    Aug 6, 2019 at 23:33
  • $\begingroup$ My apologies for not being more clear. Questions on topics like confidence intervals and Chi Squared are better suited for the site Cross Validated. Said another way, questions about the statistical underpinnings of ML/Data Science related topics are better suited there. Cheers. $\endgroup$
    – Ethan
    Aug 7, 2019 at 20:21
  • $\begingroup$ I think the significance of a prediction is a data science topic. How confident are we in the logistic regression model assigning a 0.75 to a scenario? $\endgroup$
    – user79134
    Aug 7, 2019 at 20:48

2 Answers 2

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Good question. By convention, the null hypothesis is always framed to say there is no statistical relationship between one or more independent variables and a dependent variable. This is typically tested at the p < 0.05 level. The level of the relationship beyond it being significant is not addressed in a null hypotheses. (See, for example, Encyclopedia of Research Design, edited by N.J. Salkind, 2010). As for testing the "70% confidence" result, there is no way to do that. That is the statistical result. The overall validity of a logistic regression model can be assessed using Pearson's chi-squared, R-square, and classification accuracy.

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A predictive model utilizing logistic regression cannot predict that at least one customer [...]

You cannot test if something cannot be done. All you can do is to prove the opposite, which is exactly what the alternative hypothesis is used for.

Therefore, this null hypothesis is not testable.

The alternative hypothesis would be:

A predictive model utilizing logistic regression can predict that at least one customer [...] with more than 70% confidence.

This can be tested. You build a model and if you succeed, you proved the alternative hypothesis and reject the null hypothesis.

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