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I have in my possession the answers to an annual survey of 21,030 departing passengers with information on the amount of their purchases, their destination, the reason for travel etc. After a few weeks, I estimated the turnover generated by each passenger leaving and I now have the task of analyzing the possible correlations between the Estimated turnover and the remaining variables (trip reason for example)

So I am looking for a link between a quantitative variable (variable to explain) and a qualitative variable (explanatory variable) the most logical for me would be to make an ANOVA.

However, my tutor asked me something else:

Consider the possible choices of travel pattern (tourism, business, visit) as binary variables and build a "model" like this:

Y = alpha (binary tourism variable) + beta (binary business variable) + gamma (binary visit variable) + E

with - for example the tourist binary variable equal to TRUE if the passenger to "Tourism" - E residue - Y variable to explain (Turnover)

For my part, the binary variables evoke a logistic regression but in this case it would rather have a binary variable to explain and not explanatory (as before)

So my question is: is there a way to have the same model as my tutor wanted or should I rather consider the reason for travel as a binary variable to explain and the turnover Estimated as an explanatory variable, proceed to a Logistic regression and then deduce if a link exists between these two variables? (Being aware that this will be the turnover that will depend on the reason for travel and not the travel reason that will depend on the turnover)

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If you estimate the model your tutor proposes with linear regression, you're effectively doing an ANOVA (see for example here). There is no reason why you shouldn't be able to include binary variable as explanatory variables in a linear regression. The only thing is that you would need to exclude one of them as a reference level (unless you have visitors with no reason for traveling).

Turning things upside down, that is taking for example tourism as a dependent and turnover as independent only makes sense if you're interested in questions like what is the probability that someone has a tourist destination given that they spend X$. Of course if you find a link there, you're almost certain to find one in your linear regression too, but it seems like unnecessary hassle.

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  • $\begingroup$ I didn't see it like this. Thank you ! $\endgroup$
    – blabla
    Commented Jun 21, 2017 at 9:27

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