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(a) Construct a scatter plot. (Comment on your graph.)

16 / 01 / 2019 Statistics

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Before commencing this assignment, it is important to read the section on Simple Linear Regression, Assumptions of Regression and Residual Analysis from Chapter 12, Levine. (See your Custom Publication – p308-313, p324-328 and p346) The material from Topics 5, 6, 7 and 8 also contains useful background information.
Zagat’s publishes restaurant ratings for various locations in the United States. The file Restaurants contains the Zagat rating for food, décor, service and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York. 

Part A: Summated Ratings and Cost.
(a)    Construct a scatter plot. (Comment on your graph.)
(b)    Assuming a linear cost relationship, state the regression coefficients bo and b1. (Include your Excel output.)
(c)    Interpret the meaning of the Y intercept, bo, and the slope, b1, in this problem.
(d)    Write down the simple linear regression equation, and predict the cost per person for a restaurant with a summated rating of 50.

Part B: Summated Ratings and Cost.
Perform a residual analysis for these data. Evaluate whether the assumptions of regression (L.I.N.E.) have been seriously violated. 
Included in this evaluation, you will need to use Excel to create: 
•    a residual plot, and comment on the plot, 
•    histogram (of residuals) and comment on the histogram,
•    boxplot (of residuals) and 5 number summary, and comment on the boxplot, and 
•    a normal probability plot (of residuals) and comment on the plot.
NOTE: It is essential that each component above is interpreted in relation to the given question.
Summarise your results.
You must include all Excel results for this data as part of the justification for your conclusions. (Include them within the appropriate section – not at the end of your document.)
Your assignment must be submitted as a single word document via LMS.
You will find the data in Restaurants in LMS under Topic 5, Data Files. (Use only the data that you need.)
1Based on Question 6.25 in Levine et al (2013)

Further comments:
Your completed assignment needs to include the following components:
•    An introduction, where the key aspects of this topic are fully discussed. (This discussion should be referenced using the Chicago referencing method)
•    The body of your assignment, where all of your findings are presented. (This should include relevant Excel results, graphs, tables…) Each of the pieces of information that are included need to be discussed in relation to the given question.
•    A Conclusion, which summarises your key findings and links these back to the introduction.
•    A bibliography which includes all resources referenced within your assignment.

Marks will be allocated according to the quality of each of the components above. The interpretation and discussion of your data is an essential aspect of this assignment. (It is not enough to simply include the Excel graphs or summary data.) 

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