A high-end restaurant in the city of LA, wants to understand how it improve its business. For this purpose, it samples 30 customers who visit it. A consultant is hired by the restaurant owner to provide insights into what can drive business higher and what can be done to attract new customers. So the research problem is to determine variables/ aspects that can deliver more business. The owner believes that a customer who spends more on his visit tends to a repeat customer delivering more business. Such a customer also pays a handsome tip. The restaurant request its customers to fill in a feedback form if possible. This asks many questions from the customer which can be used by the consultant.
Based on this feedback from the owner, the consultant provides the following research model.
Ratings = f( average tip per person, ambience ratings, bill amount, online ratings, spending on alternate restaurants by the customer). This is a linear regression model where the dependent variable is ratings provided by the customer on the feedback form. These ratings are taken as a proxy for customer pull. Better ratings implies more business.
Ratings are assumed to be dependent on :
Average tip per person = Tip paid per bill / number of seats for the bill.
Ambience ratings: Ratings on a number of aspects by the customers on the feedback form. These include services offered, lighting on the table, general environment in the restaurant, degree of hospitality, etc. these are complied into a single index by the consultant and labeled ambience ratings.
Bill amount: This refers to the total bill amount exclusive of taxes
Online ratings: these refer to the ratings given by customers on the restaurant site on the Internet.
Spending on alternate restaurants by the customer. The feedback form gathers information on alternate spending by the customer on competitor’s restaurant in the last 6 months. This variable is included to gauge the impact of competition on our business.
The consultant hypothesizes that:
Higher is the tip, greater are the ratings
A better ambience leads to better business
A customer with a larger bill amount would lead to more business.
Higher online ratings must lead to more customers, so that existing customers must be encouraged to give online reviews and ratings.
The effect of spending on competitor restaurant cant be outlined and needs investigation.
The descriptive analysis shows the mean, standard deviation, variance, median , mode, skewness , kurtosis and coefficient of variation for all variables.
CORRELATIONAL ANALYSIS :
Correlation tell us how two variables are associated. We show the correlation matrix in the appendix which can be used to conclude that:
Overall ratings are positively associated with ambience ratings, Bill amount and online ratings. This makes sense as a customer who likes the restaurant is likely to give high overall ratings as well as a high rating on the online option. Since ambience is part of the total experience of dining, high ambience ratings by a customer are associated with high overall ratings. Since this is a high end restaurant we would expect such a customer to have a high bill as this allows her to sample different cuisines ( rather than stick to a small expenditure) .
Overall ratings are negatively associated with the tip paid and with the spending on alternate restaurants. A regular customer who likes this restaurant is likely to visit other restaurants so that the negative association is understandable. The relation with tipping tells us that tipping may be looked down at by customers, so that workers can be trained to decline/ discourage tips. The management can also make it a policy that individual tipping is not allowed.
The correlation does not tell us about the cause and effect. It only deals with association and not causation. The correlation matrix can be confirmed with a scatter plot as shown for three variables in the appendix.
A simple linear regression is done. This leads us to the following estimated equation:
Ratings= 55.26 -17.499*Tip +328.8322468*Ambience ratings +.126*Bill +.0244*online R – .0938*SPA. This tells us ( based on the sign of the cff) that
Ratings and average tip amount are negatively related. This would imply that large tips must be discouraged. A $1 rise in per person tip decreases ratings by 17.499
Ambience ratings are positively affecting overall ratings. The restaurant needs to improve its ambience ratings and all factors that combine to arrive at the ambience ratings. A 1 point rise in ambience ratings gives marginal ratings of 328.8322.
Higher the bill amount higher is the overall ratings. For every dollar spent ratings rise by 0.126
Higher are online ratings greater are overall ratings. A 1 point rise in online ratings causes overall ratings to rise by 0.0244.
Higher is the spending on alternate eating places lower are the overall ratings for this restaurant. This shows that competition is strong. For every dollar spent on competition the overall ratings fall by 0.0938.
We can test each coefficient for its significance using a t test and an overall F test for the overall regression model itself.
We use a p value test for significance. Assume that we choose a 5% level of significance. If the p value >.05 we conclude that the cff is not significant. If the p value < .05 then the cff is significant in a statistical manner. Based on this rule we observe that 2 variables are not significant. These include online ratings and spending on alternate restaurants. The p value of online ratings cff is 0.429 > .05. This implies that online ratings have insignificant role in overall ratings and therefore in getting new business.
The p value of alternate restaurant spending is 0.144 >.05. This would imply that there is no real competition with alternate restaurants. The clientele for this restaurant is specific and does not depend on what the competition has to offer.
The cffs of all other explanatory variable are significant as the p value is < .05.
We can also test for the overall significance of the model using the F test. As the results show the p value of the F test value is 1.3649E-09. This is very low and shows that the overall model is statistically significant. This corroborates the R2 value of 0.84. This implies a high value of R2, which is also called the coefficient of determination. It tells us the % of variation in the dependent variable that can be explained by the independent variables. In our case 84.06% of variation in the overall ratings can be explained by the independent explanatory variables.
The linear model postulated by the consultant was good as it gave a significant relationship. It tells us that certain factors like ratings for ambience, amount of bill and average tip per customer are important variables that drive overall ratings and therefore good business. Higher ratings are an indicator /proxy for new customers.
The model can be improved by bringing in new variables like specific ratings on food quality, no of times a customer dines here, no of times the customer eats out of home, income level of customer, marital status/ number of kids and other variables. These may help to improve the predictive power of the model.
Within this model the results show that the owners need to focus on ambience and get new customers who order large amounts. The owners need not spend any money on improving online ratings as they are insignificant. The owners need to build further on the exclusivity of the restaurant as customer spend on other restaurants is also insignificant in explaining overall ratings and business.
ratings overall average tip per person ambience ratings Bill amount online ratings spending on alternate restaurant
ratings overall 1
average tip per person -0.678233971 1
ambience ratings 0.356752299 0.113846089 1
Bill amount 0.419316325 0.069764701 0.1477934 1
online ratings 0.036329711 -0.22154346 -0.2636172 -0.2641712 1
spending on alternate restaurant -0.608732054 0.481957971 -0.0437954 -0.2962957 -0.156364776 1
Multiple R 0.916839769
R Square 0.840595163
Adjusted R Square 0.809940387
Standard Error 4.718128042
df SS MS F Significance F
Regression 5 3052.096 610.4192 27.42134 1.3649E-09
Residual 26 578.77904 22.26073
Total 31 3630.875
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 55.26318738 21.29892914 2.59464629 0.01535715 11.48261196
average tip per person -17.49919152 2.466198484 -7.0956136 1.55345E-07 -22.56853506
ambience ratings 328.8322468 69.65896631 4.72060187 7.02705E-05 185.6461923
Bill amount 0.126038647 0.029282701 4.30420149 0.000210704 0.065847193
online ratings 0.024436149 0.030422233 0.80323324 0.429122301 -0.038097646
spending on alternate restaurant(SPA) -0.093809919 0.062303487 -1.5056929 0.144199498 -0.221876569