# logistic regression vs OLS - comparison of variable significance

I am modeling usage of a particular app like this: predicting week 3 engagement (number of days of the week the product is used) based on prior engagement (week 1 and week 2) and usage of particular product features in week 2.

In the first step, I do an ordinary least squares regression. The model performs well with R^2 of 0.6 and 11 of the 21 variables are highly significant.

Since my dependent variable is actually bounded (by 7), I divide it by 7 and do a logistic regression with the same variables. Now, only 5 variables are significant.

I realise the interpretation of the coefficients is different, but why should 6 variables previously significant in OLS not be significant in the logistic regression? Could it be the multi-collinearity (usage of different features are highly correlated) that poses a problem in OLS but not in logistic regression? I can't find any article that talks about that. • When your logit outcome is not strictly binary, it is very common for statistical software to treat all the non-zero values as one, in which case you are modeling the "don't use app" versus "use app some" decision, rather than a continuous measure of usage intensity. If that is the case here, the two models are pretty different and it is not surprise that they don't "agree". You might want to use fractional response model if you want an apples-to-apples comparison with OLS. – Dimitriy V. Masterov Aug 2 at 22:15
• Or it may be interpreting them as proportions – user0 Aug 3 at 0:31
• is the output from OLS valid, given that the y values are bounded? – vvv Aug 5 at 18:06