STAT 503X Case Study 1 Restaurant Tipping 1 Description Food server s tips in restaurants may be influenced by many factors including the nature of the restaurant size of the party table locations in the restaurant To make appropriate assignments which tables the food server waits on for the food servers restaurant managers need to know what these factors are For the sake of staff morale they must avoid either the substance or appearance of unfair treatment of the food servers for whom tips are a major component of pay In one restaurant a food server recorded the following data on all customers they had served during a interval of two and a half months in early 1990 The restaurant located in a suburban shopping mall was one of a national chain and served a varied menu In observance of local law the restaurant offered seating in a non smoking sections to patrons who requested it The data was assigned to those days and during those times when the food server was routinely assigned to work The data available are TOTBILL TIP SEX SMOKER DAY TIME SIZE Total bill including tax in dollars Tip in dollars Sex of person paying bill 0 male 1 female Smoker in party 0 No 1 Yes 3 Thur 4 Fri 5 Sat 6 Sun 0 day 1 night Size of the party This is a great data set in many ways because it is clearly a pilot study There should be no temptation to make inference from the data and emphasis should be on poking around the data to formulate hypotheses and design a careful study 1 2 Suggested Approaches Approach Data Restructuring Make new variable Tip Rate from Tip Total Make dummy variable for day of the week Summary statistics marginal and conditional Reason Type of questions addressed Tip is usually referred to by percentage points or as a rate This also calibrates the variable according to the bill total and allows us to compare values across the other variables such as size of the party This is a categorical variable so it is not appropriate to treat it as an ordinal value This is especially important for a regression analysis extract location scale information Histograms with different bin widths explore univariate distributions Pairwise Scatterplots marginal and conditional Mosaic Plots explore bivariate distribution and correlation structure What is the average tip rate at the restaurant Are tips higher on Saturdays than on Thursdays What is the average party size Are there unusual patterns in the tipping behavior Outliers distribution shape quirky structures Are there unusual patterns in the tipping behavior explore multivariate categorical distributions Determining the most important factors to tip rate Are there dependence relationships between the categorical variables Which factors contribute to higher tips Regression We don t have to do anything really sophisticated with this data It is almost entirely categorical except for tip and total bill So we will make extensive use of conditional plots 2 3 Actual Approaches 3 1 Summary Statistics Number of Observations 244 Number of Variables 7 Mean SD TOTBILL 19 78 8 90 TIP 3 00 1 38 TIPRATE 16 1 6 1 SEX 0 36 0 48 SMOKER 0 38 0 49 TIME 0 72 0 45 SIZE 2 57 0 95 Table 1 Averages and Standard Deviations of Variables The average bill is 20 average tip is 3 and average tip rate is 16 There are less females that pay the bill than males less smokers than non smokers and more dining parties are in the restaurant at night than during the day The average number of diners per party are 2 5 Tip Rate Total Number Total Day Night Thurs 16 1 62 16 1 61 16 0 1 Fri 17 0 19 18 9 7 15 9 12 Sat 15 3 87 0 15 3 87 Sun 16 7 76 0 16 7 76 Table 2 Tip Rate total number of diners broken down by Day of the week and Time of Day Over the days of the week Friday has very few diners and Saturday has the most diners There are no dining parties for lunch on the weekends During the week there are more dining parties for lunch than dinner but on weekends there are more dining parties for dinner The lowest tip rate occurs on Saturday night The highest is Friday lunch but there were only 7 dining parties then Tip Rate Total Number Non Smoker Smoker Total Male 16 1 97 15 3 60 15 8 157 Female 15 7 54 18 2 33 16 6 87 Total 15 9 151 16 3 93 16 1 244 Table 3 Tip Rate total number of diners broken down by Sex and Smoker The average tip rate paid by females is higher than that paid by males non smokers is lower than for smokers But note that female smokers gave the highest average tip and that male non smokers paid a higher average tip rate than did female non smokers 3 Size of Party Tip Rate Total Number 1 21 7 4 2 16 6 156 3 15 2 38 4 14 6 37 5 14 1 5 6 15 6 4 Table 4 Tip Rate total number of diners broken down by Size of the Party The most dining parties were of size 2 and there were very few dining parties of size 1 5 or 6 Parties of size 2 3 and 4 show a decreasing trend in tip rate as size increases Total Tip Tip Rate Sex Smoke Day Time Size Total 1 00 Tip 0 68 1 00 Tip Rate 0 34 0 34 1 00 Sex 0 14 0 09 0 07 1 00 Smoke 0 09 0 01 0 03 0 00 1 00 Day 0 17 0 14 0 01 0 23 0 03 1 00 Time 0 18 0 12 0 03 0 21 0 05 0 87 1 00 Size 0 60 0 49 0 14 0 09 0 13 0 17 0 10 1 00 Table 5 Correlations between variables Tip and total bill are moderately highly correlated There is a strong correlation between day and time 3 2 3 2 1 Histograms of tips varying bar width 1 barwidth The shape of the data is skewed to the right which says that there are more small tips and fewer large tips It is unimodal with a peak at 1 2 and gradually falling off to the right This says that there are more groups of diners that pay tips in the range 1 4 Assuming there is a relationship between tip and total bill this suggests that the total bills may be mostly 15 60 roughly It suggests the restaurant is not an expensive one There are very few tips less than 1 3 2 2 0 50 barwidth It is no longer unimodal but bi or even tri modal There is more to the tipping habits than implied by the large barwidth of 1 Also several very high tips are now apparent in the data These are outliers but from a waiting perspective these are the …
View Full Document