Zagat’s Publishes Restaurant Ratings for USA Location Case Study

Question: Write an essay on restaurant ratings for various locations in the United States. Answer: The report discusses about the Zagats publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, dcor, service and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York. The analysis on the data sets is done to determine the summated ratings and the costs of restaurant meals in the New York City and its surrounded areas. The report briefly explains the restaurant industry, its cost structure, its relationship with customers and their satisfactions, the quality of meals provided and moreover the correlation between costs of restaurant meal and services with the summated restaurant ratings. The assignment is done through simple linear regression for determining the correlation among the chosen variables. The New York City is full of these types of restaurants. Due to the citys huge diversity and spread, the restaurants are one of the biggest industries in that parti cular region. As there is diversified population staying and wandering, many tastes and types of restaurant meals are available in the NYC. Therefore, this report will broadly show with the data analysis that how the summated ratings of those restaurants are important in relation with the restaurant cost of meal. Data analysis and interpretation: Summated ratings and Costs of Restaurant Meals Zagats publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, dcor, service and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York. On the given data, a quantitative data analysis is done by simple linear regression taking the two variables as summated ratings and the cost of meals in the restaurants. Regression is the technique that interprets the relationship between two or more variables (Montgomery, Douglas, Elizabeth Peck, and Geoffrey 2015). Here the simple linear regression technique is applied to interpret the relationship between the two variables.Firstly, to show the relationship between the summated rating and cost of meals in the restaurant, the scatter plot is done by taking the dependent variable to be the summated ratings and independent variable being the cost of meals. Table 1: Plate gap and tear: Plate Gap Tear 0.00 0.00 0.00 0.00 1.80 0.45 1.80 0.85 0.00 0.35 0.00 0.30 0.00 0.70 0.00 1.90 0.00 0.25 -1.80 0.10 -1.80 0.15 3.00 3.90 -1.80 0.00 0.00 0.55 -3.00 0.00 -1.80 0.05 1.80 0.40 1.80 4.30 0.00 0.00 The above scatter plot shows a linear and positive trend line which is upward sloping. This means the relationship between the two variables is positive and increasing i.e. the high the value of number of plates, the high will be the rating in terms of the reviews. The rise in plates means rise in production and rise in revenue by the restaurant too. Therefore, this will cause higher ratings. The regression output is found through simple linear regression analysis that is given below: Table 2: Simple Linear Regression Output: SUMMARY OUTPUT Regression Statistics Multiple R 0.617347283 (correlation coefficient - strenght and direction of relationship (exel does not give us the sign) - from scatterplot we know it is positive R Square 0.381117667 (coefficient of determination) Adjusted R Square 0.344712824 Standard Error 1.024120857 Observations 19 ( ANOVA df SS MS F Significance F Regression 1 10.98 10.98 10.46887269 0.004860746 Residual 17 17.83 1.048823529 Total 18 28.81 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept (b0) 0.75 0.234949438 3.192176183 0.00533663 0.254300016 1.2457 0.2543 1.2457 Plate Gap (b1) 0.5 0.154532576 3.235563736 0.004860746 0.173964763 0.826035 0.173965 0.826035 Now, it is assumed and shown that the two variables are having a linear cost relationship. Therefore, the values of the coefficients b0 and b1 are- 0.75 and 0.5 respectively. According to the question when plate gap (x) increases by 1 unit, the predicted value of tear rating (y) increases by 0.5 units. Therefore, b0 and b1 have relationship which is greater than zero i.e. positive. A rise in plate gap of 1 unit will cause the tear rating increase of 0.5 units. At the same time, the positive intercept means that the curve starts from a positive value with positive slope. Predicted Y = 0.75 + 0.5x Predicted Tear rating = 0.75 + 0.5 (plate gap) When plate gap is 0, y = mx + c -- 0.75 + 0.5(0) = 0.75 It means that when plate gap (x) is zero, it means we are looking at the intercept, b0. Predicted tear rating = 0.75 + 0.5 (0) = 0.75 Therefore, the estimated simple linear regression equation is given by: Predicted Y = 0.75 + 0.5x Now, when the rating is 50, the predicted value of cost per plate is given by: 50= 0.75 + 0.5 (cost per plate) 50-0.75= 0.5x 5 x = 49.25 x= 49.25/0.5 x= 98.50 Here the residual analysis is done with the data on size of the restaurant and the value of rent. The data is given in the table below: Size Rent 850 950 1450 1600 1085 1200 1232 1500 718 950 1485 1700 1136 1650 726 935 700 875 956 1150 1100 1400 1285 1650 1985 2300 1369 1800 1175 1400 1225 1450 1245 1100 1259 1700 1150 1200 896 1150 1361 1600 1040 1650 755 1200 1000 800 1200 1750 Table 3: Size and rent data on restaurants: The above data shows a linear relationship with a positive trend. This means the size effect has a rising trend with the rent of a restaurant. Positive relationship indicates an increasing trend which means as size of a restaurant rises, the value of rent also rises. This has direct relationship with cost as rent is the fixed cost included in the total cost factor. Therefore, as size of the restaurant increases, the rent increases thereby increasing the total cost. Thus, the ratings will be affected with this cost value. If the cost is not overcome with the revenue and if the number of plates served is not high, the ratings will fall. This means rise in cost may cause fall in the total profit as well as the summated ratings regarding the restaurant meals. The summary output of regression analysis is given as below: Table 4: Summary output of regression between size of the restaurant and rent SUMMARY OUTPUT Regression Statistics Multiple R 0.850060796 R Square 0.722603356 Adjusted R Square 0.710542633 Standard Error 194.5953946 Observations 25 ANOVA df SS MS F Significance F Regression 1 2268777 2268777 59.91376 7.52E-08 Residual 23 870949.5 37867.37 Total 24 3139726 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept (b0) 177.1208202 161.0043 1.1001 0.28267 -155.942 510.1835 -155.942 510.1835 Size (b1) 1.065143906 0.137608 7.740398 7.52E-08 0.780479 1.349809 0.780479 1.349809 The above output indicates a predicted value for the size and rent equation, which is: From output, can see that b0= 177.12, andb1= 1.0651(x) Predicted rent = 117.12 + 1.0651 (Size) When the size of the apartment increases by 1 square feet, the predicted rent increases by $1.065 Y = mx + c -- Y = 177.1208 + 1.0651 (1000) = $1242.12 Predicted rent = 177.12 + 1.0651 (1000) = $1242.12 The histogram is formed regarding the values: Bin range Frequency Cumulative % 500 0 0.00% 1000 13 26.00% 1500 26 78.00% 2000 10 98.00% More 1 100.00% The cumulative frequency shows a rising manner. This rising frequency is shown in the linear trend equation. Positive relationship indicates an increasing trend which means as size of a restaurant rises, the value of rent also rises. This has direct relationship with cost as rent is the fixed cost included in the total cost factor (Cameron, Colin and Trivedi 2013). Therefore, as size of the restaurant increases, the rent increases thereby increasing the total cost. Thus, the ratings will be affected with this cost value. If the cost is not overcome with the revenue and if the number of plates served is not high, the ratings will fall. This means rise in cost may cause fall in the total profit as well as the summated ratings regarding the restaurant meals. The data is shown through the histogram presentation above. The above diagram is the representation of asking rest with the predicted rent of the restaurant. The values show rising manner in the data above. Data interpretation Now, taking all the outputs, summarized results can be found from the regression analysis. The regression results for size effects with the rent are given below: Regression Statistics Multiple R 0.850060796 R Square 0.722603356 Adjusted R Square 0.710542633 Standard Error 194.5953946 Observations 25 The above value of multiple R is 0.850060796, near to 1. Generally, the value of correlation coefficient i.e. R lies between -1 to 1. At the same time, the value of R square is 0.722603356. However, the value of R in this case is high, near to 1, meaning that there is a high correlation between the results for size effects with the rent (Chatterjee, Samprit and Hadi 2015). This has direct relationship with cost as rent is the fixed cost included in the total cost factor. Therefore, as size of the restaurant increases, the rent increases thereby increasing the total cost. Thus, the ratings will be affected with this cost value. If the cost is not overcome with the revenue and if the number of plates served is not high, the ratings will fall. This means rise in cost may cause fall in the total profit as well as the summated ratings regarding the restaurant meals. ANOVA df SS MS F Significance F Regression 1 2268776.545 2268777 59.91376 7.52E-08 Residual 23 870949.4547 37867.37 Total 24 3139726 In the ANOVA output, the value of F statistic is also significant. Therefore, the variances are compared between the two variables i.e. size of the restaurant and rent, has a low variability. This also indicates a direct relation between them. Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept (b0) 177.1208202 161.0042766 1.1001 0.28267 -155.942 510.1835 -155.942 510.1835 Size (b1) 1.065143906 0.137608412 7.740398 7.52E-08 0.780479 1.349809 0.780479 1.349809 The values of intercept are signified by the above results. The value of standard error is high. The t statistic is higher than 1, meaning a highly significant relationship between the variables (Draper, Norman and Harry Smith 2014). The p-value is low. The low value of p signifies the model to be more significant. Therefore, the overall data structure indicates a good fitted model on which the cost should be reduced in order to make profit in the restaurants as size of the restaurant directly affects the rent and thereby the fixed cost. Conclusion: The report has dealt with the Zagats publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, dcor, service and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York. The analysis on the data sets is done to determine the summated ratings and the costs of restaurant meals in the New York City and its surrounded areas. All the above data has indicated a positive relationship with the summated ratings in terms of cost of the restaurant. To eradicate or reduce the cost, the size factor should be taken into account, as the rise in size causes a rise in the cost. Moreover, the relationship between the plates served and the ratings are calculated which gives a clear picture that as there is more plates served, the ratings are high. As there is diversified population staying and wandering, many tastes and types of restaurant meals are available in the NYC. Therefore, t his report shows broadly with the data analysis that how the summated ratings of those restaurants are important in relation with the restaurant cost of meal. References: Cameron, A. Colin, and Pravin K. Trivedi.Regression analysis of count data. Vol. 53. Cambridge university press, 2013. Chatterjee, Samprit, and Ali S. Hadi.Regression analysis by example. John Wiley Sons, 2015. Draper, Norman R., and Harry Smith.Applied regression analysis. John Wiley Sons, 2014. Montgomery, Douglas C., Elizabeth A. Peck, and G. Geoffrey Vining.Introduction to linear regression analysis. John Wiley Sons, 2015.