Restaurant Digest, a famous restaurant magazine writes that the amount of tips servers get in Florida is affected by several factors including the amount of bill, number of adult diners as well as kids and the income of the diners. Use the data below to answer the following questions: Find the multiple regression model. At a level of significance of 0.03, is there a significance relationship between the amount of tip and at least one of the independent variables? What is the likely amount of tip if a group of diners spend $40.33 and had an annual income of $81,000. The diners included 4 adults and 3 kids? What percent of the variation in amount of tip is accounted for by amount of bill, annual income, number of adults and kids?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Restaurant Digest, a famous restaurant magazine writes that the amount of tips servers get in Florida is affected by several factors including the amount of bill, number of adult diners as well as kids and the income of the diners. Use the data below to answer the following questions:
- Find the multiple regression model.
- At a level of significance of 0.03, is there a significance relationship between the amount of tip and at least one of the independent variables?
- What is the likely amount of tip if a group of diners spend $40.33 and had an annual income of $81,000. The diners included 4 adults and 3 kids?
- What percent of the variation in amount of tip is accounted for by amount of bill, annual income, number of adults and kids?
| Customer | Amount of Tip | Amount of Bill | Number of adult Diners | Number of kids | Annual Income |
| 1 | $ 7.00 | $ 48.97 | 5 | 3 | 100000 |
| 2 | $ 4.50 | $ 28.23 | 4 | 3 | 80000 |
| 3 | $ 1.00 | $ 10.65 | 1 | 0 | 20000 |
| 4 | $ 2.40 | $ 19.82 | 3 | 2 | 19000 |
| 5 | $ 5.00 | $ 28.62 | 3 | 2 | 50000 |
| 6 | $ 4.25 | $ 24.83 | 2 | 2 | 25000 |
| 7 | $ 0.50 | $ 6.24 | 1 | 1 | 8000 |
| 8 | $ 6.00 | $ 49.20 | 4 | 3 | 106000 |
| 9 | $ 5.00 | $ 43.26 | 3 | 2 | 98000 |
| 10 | $ 4.75 | $ 31.36 | 4 | 3 | 60000 |
| 11 | $ 5.25 | $ 32.87 | 4 | 3 | 61000 |
| 12 | $ 6.00 | $ 34.99 | 3 | 2 | 63000 |
| 13 | $ 4.00 | $ 33.91 | 4 | 2 | 62000 |
| 14 | $ 3.35 | $ 23.06 | 2 | 1 | 25000 |
| 15 | $ 0.75 | $ 4.65 | 1 | 1 | 5000 |
| 16 | $ 3.30 | $ 23.59 | 2 | 1 | 30000 |
| 17 | $ 3.50 | $ 22.30 | 2 | 1 | 28000 |
| 18 | $ 3.25 | $ 32.00 | 2 | 1 | 48000 |
| 19 | $ 5.40 | $ 50.02 | 4 | 3 | 108000 |
| 20 | $ 2.25 | $ 17.60 | 3 | 3 | 18000 |
| 21 | $ 5.50 | $ 44.47 | 4 | 3 | 90000 |
| 22 | $ 3.00 | $ 20.27 | 2 | 2 | 20000 |
| 23 | $ 1.25 | $ 19.53 | 2 | 2 | 19000 |
| 24 | $ 3.25 | $ 27.03 | 3 | 3 | 28000 |
| 25 | $ 3.00 | $ 21.28 | 2 | 4 | 33000 |
| 26 | $ 6.25 | $ 43.38 | 4 | 3 | 88000 |
| 27 | $ 5.60 | $ 28.12 | 4 | 3 | 40000 |
| 28 | $ 2.50 | $ 26.25 | 2 | 2 | 41000 |
| 29 | $ 9.25 | $ 56.81 | 5 | 4 | 120000 |
| 30 | $ 8.25 | $ 50.65 | 5 | 4 | 110000 |
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