# Maximizing your tip as a waiter (Part 2)

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In Part 1 of “Maximizing your tip as a waiter”, I talked about a **target-based categorical encoder** for Statistical/Machine Learning, firstly introduced in this post. An example dataset of `tips`

was used for the purpose, and we’ll use the **same dataset** today. Here is a snippet of `tips`

:

Based on these informations, how would you maximize your **tip** as a waiter working in this restaurant?

# 1 – Descriptive analysis

The tips (available in variable `tip`

in `tips`

) range from 0 to 10€, and are **mostly comprised between 2 and 4€**:

Another interesting information is the **amount of total bills**, which is comprised between 3 and 50€, and mostly between 10 and 20€:

Both distributions – of tips and total bill amounts – are **left-skewed**. We could fit a probability distribution to each one of them, such as lognormal or Weibull, but this would not be extremely informative. We would be able to derive some confidence intervals or things like the **probability of having a total bill higher than 40€** though. Generally, in addition to `tip`

and `total_bill`

, we have the following raw information on the **marginal distributions of other variables**:

A transformation of `tips`

dataset using a one-hot encoder (cf. the beginning of this post to understand what this means) allows to obtain a dataset with numerical columns at the expense of creating a larger dataset, and to **derive correlations**:

Some correlations mean nothing at all. For example, the correlation between `daySat`

and `dayThur`

or `sexMale`

and `timeLunch`

. The most interesting ones are those between `tip`

and the other variables. Tips in € are more positively correlated with total bills amounts, and with the number of people dining at a table. Here, contrary to the previous post and for a learning purpose presented later, we will categorize our tips in **four classes**:

**Class 0**: tip in a ]0; 2] € range –**Low****Class 1**: tip in a ]2; 3] € range –**Medium****Class 2**: tip in a ]3; 4] € range –**High****Class 3**: tip in a ]4; 10] € range –**Very high**

We’ll hence be considering a **classification problem**: how to be in class 2 or 3 given the explanatory variables?

**Class 0**, **low tip** contains 78 observations. **Class 1**, **medium tip** contains 68 observations. **Class 2**, **high tip** contains 57 observations. **Class 3**, **very high tip** contains 41 observations. Below, as an **additional descriptive information related to these classes**, we present a distribution of tips (in four classes) as a function of explanatory variables **smoker**, **sex**, **time**, **day**, **size** and **total bill** (with the total bill being segmented according to its histogram breaks):

According to this figure, the fact that the table is reserved for smokers or not, doesn’t highly affect the **median tip**. The same remark holds for the **waiter’s sex** and the **time of the day** when the meals are served (dinner or lunch), which both don’t seem to have a substantial effect on median amounts of tips.

Conversely, **Sunday seems to be the best day for you to work** if you want to maximize your tip. The **number of people dining at a table, and total bills amounts are other influential explanatory variables for the tip**: the higher, the better. But unless you can choose the table you’ll be assigned to (you’re the boss, or his friend!), or are great at embellishing and advertising the menu, your influence on these variables – **size** and **total_bill** – will be limited.

In section 2 of this post, we’ll study these effects more systematically by using a statistical learning procedure; a procedure designed for accurately classifying tips within the four classes we’ve just defined (low, medium, high, very high), given our explanatory variables. More precisely, we’ll study the effects of the numerical target encoder on a Random Forest’s accuracy.

# 2 – Encoding using mlsauce; cross-validation

**Import Python packages**

import requests import nnetsauce as ns import mlsauce as ms import numpy as np import pandas as pd import querier as qr from sklearn.model_selection import cross_val_score from sklearn.ensemble import RandomForestClassifier from tqdm import tqdm

**Import tips**

url = 'https://github.com/thierrymoudiki/querier/tree/master/querier/tests/data/tips.csv' f = requests.get(url) df = qr.select(pd.read_html(f.text)[0], 'total_bill, tip, sex, smoker, day, time, size')

**Create the response (for classification)**

# tips' classes = response variable y_int = np.asarray([0, 0, 2, 2, 2, 3, 0, 2, 0, 2, 0, 3, 0, 1, 2, 2, 0, 2, 2, 2, 3, 1, 1, 3, 2, 1, 0, 0, 3, 1, 0, 1, 1, 1, 2, 2, 0, 2, 1, 3, 1, 1, 2, 0, 3, 1, 3, 3, 1, 1, 1, 1, 3, 0, 3, 2, 1, 0, 0, 3, 2, 0, 0, 2, 1, 2, 1, 0, 1, 1, 0, 1, 2, 3, 1, 0, 2, 2, 1, 1, 1, 2, 0, 3, 1, 3, 0, 2, 3, 1, 1, 2, 0, 3, 2, 3, 2, 0, 1, 0, 1, 1, 1, 2, 3, 0, 3, 3, 2, 2, 1, 0, 2, 1, 2, 2, 3, 0, 0, 1, 1, 0, 1, 0, 1, 3, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 2, 3, 3, 3, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 3, 3, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 3, 0, 0, 3, 2, 3, 2, 2, 2, 0, 0, 2, 2, 2, 3, 2, 3, 1, 3, 2, 0, 2, 2, 0, 3, 1, 1, 2, 0, 0, 3, 0, 0, 2, 1, 0, 1, 2, 2, 2, 1, 1, 1, 0, 3, 3, 1, 3, 0, 1, 0, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 3, 3, 0, 0, 0, 1])

**Obtain a distribution of scores, using encoding**

Here, we use `corrtarget_encoder`

from the mlsauce to **convert categorical variables (containing character strings) to numerical variables**:

n_cors = 15 n_repeats = 10 scores_rf = {k: [] for k in range(n_cors)} # accuracy scores for i, rho in enumerate(np.linspace(-0.9, 0.9, num=n_cors)): print("\n") for j in range(n_repeats): # Use the encoder df_temp = ms.corrtarget_encoder(df, target='tip', rho=rho, seed=i*10+j*10)[0] X = qr.select(df_temp, 'total_bill, sex, smoker, day, time, size').values regr = RandomForestClassifier(n_estimators=250) scores_rf[i].append(cross_val_score(regr, X, y_int, cv=3).mean())

From these accuracy scores `scores_rf`

, we obtain the following figure:

**Quite low accuracies… Why is that?** With that said, the best scores are still obtained for high correlations between response and pseudo response. In Part 3 of “Maximizing your tip as a waiter”, **here are the options that we’ll investigate**:

- Compare the correlation-based encoder with one-hot’s accuracy
- Further decorrelate the numerically encoded variables by using a new
*trick*(summing different, independent pseudo targets instead of one currently) - Consider the use a different dataset if classification results remain poor on
`tips`

. Maybe`tips`

is just random? - Use the teller to understand what drives the probability of a given class higher (well, that’s definitely the laaaaast, last step)

Your remarks are welcome as usual, **stay tuned!**

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