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I would like to find out whether there is a significant relationship between No-show rates and the part of the week (weekday/weekend), this in order to be able to suggest whether restaurants should allow or not allow reservations on certain days of the week.

Am I right to think a logistic regression would be suitable for this? As you can see from the preview of my data I only have dummy variables available, and one continuous, which is making me confused about which type of regressions are possible. Or should I not use a regression at all? My main confusion I think lies in that I do not know what the outcome of my analysis should be, a yes/no answer, a p-value, i don't know :(

Preview of my dataset

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  • $\begingroup$ What does the "reservation column" denote ? $\endgroup$
    – IrishStat
    Jul 12, 2017 at 13:54
  • $\begingroup$ I think i have it.. these are transactions some of which reflected a reservation. $\endgroup$
    – IrishStat
    Jul 12, 2017 at 14:28
  • $\begingroup$ I would use a contingency table and Fisher's exact test. With the rows as weekday/weekend and the columns show/no show $\endgroup$
    – Dave2e
    Jul 12, 2017 at 14:31
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    $\begingroup$ Which would be the "continuous" variable? What does "size" mean? Why would "reservation" be relevant, when presumably "no-show" is irrelevant for someone without a reservation? $\endgroup$
    – whuber
    Jul 12, 2017 at 15:11
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    $\begingroup$ @MattBarstead i am using a dataset of over 40'000 transactions, with 1400 no-shows and 9900 cancellations, i also thought about combining them as it comes down to the same result; no customer.. $\endgroup$
    – Emily
    Jul 12, 2017 at 15:39

2 Answers 2

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From your question, it sounds like this is your main issue:

...in order to be able to suggest whether restaurants should allow or not allow reservations on certain days of the week.

To address this question, you'll want to restrict your analyses to just the people who made a reservation (folks who come in without a reservation don't contribute to your understanding of whether no-shows are more likely on certain days). You're right that you can use logistic regression for this, with whether or not the reservation no-showed (0 or 1) as the outcome (or perhaps cancellations or no-shows, as per Matt Barstead's comment), and whether or not it's a weekend and size of the reservation as predictors. I also recommend you include an interaction between weekend and size, to test whether the relationship between size of reservation and likelihood of a no-show is different on weekends vs. weekdays (or whether smaller vs. larger parties have a bigger difference between weekend and weekday no-show rates, depending on how you look at it). As always, plotting your results will make interpretation easier. Here's a relevant tutorial I wrote up a couple years ago: https://blogs.uoregon.edu/rclub/2016/04/05/plotting-your-logistic-regression-models/

If you want to examine the relationship between no-showing and weekend separately from the relationship between no-showing and reservation size, you can run two separate logistic regression models. Alternatively, you can run the no-showing and weekend model as a cross-tab analysis, if you prefer, possibly using Fisher's exact test to test the hypothesis that weekend and no-showing are unrelated.

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To begin with you provided a list of transactions. I would aggregate the transaction data to daily values. Time series data is a collection of transactions , e.g. daily totals. At this level you have a number of time series a) total # of reservatons by day b) total # of cancellations c) total # of no shows. d) composite of b and c . You may have to model different classes of "size" i.e. 0-2 , 3-5 , 5-10 , over 10 as this might be an important classifier . I surmise that size is the # of people in the reservation who will be seated ? I would not analyse percentages but I would model b , c and d as a function of a thus generating three equations and three sets of forecasts. Analysis of the coefficients could lead to insight. Note that a useful model might detect day-of-the-week effects , weekly effects , monthly effects , pre and post holiday effects , long-weekend effects , level shift effects , local time trends etc while dealing with anomalous values. An example of this kind can be found at http://autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/53-capabilities-presentation starting at slide 49 may be of some help to you.

If you search for " user:3382 :daily effects" you will find more hints (124 posts) on this subject.

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  • $\begingroup$ Providing a "down vote" without a supportive comment is in my opinion dispiriting.. $\endgroup$
    – IrishStat
    Jul 12, 2017 at 15:35
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    $\begingroup$ What advantage do you see in summarizing the transaction data into daily rates? I agree that time series could be a useful tool (identifying cyclic trends, etc.), but surely the transaction-level data are more informative than daily summaries? (I'm not your downvoter, just curious) $\endgroup$ Jul 12, 2017 at 15:52
  • $\begingroup$ Transactional data analysis can lead to estimating a probability given the specific attributes that are known but what is not in the model is the overall activity for that particular kind of day say the 15th of the month for example or a sunday before a monday holiday. In my (limited) experience a more collective approach can be used to understand and then predict activity. By the way these are not rates so much as they are counts. $\endgroup$
    – IrishStat
    Jul 12, 2017 at 15:58
  • $\begingroup$ @RoseHartman For sure there is a loss of "information" when you use an aggregate of any kind but I took the question to mean that what kind of (temporary) policy should the restaurant have in effect for particular days taking into account possible "cause variables" like is it the first week of July and tomorrow is July 4th ...etc. $\endgroup$
    – IrishStat
    Jul 12, 2017 at 16:23

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