MCD2080: Business Statistics
Assignment 2: Linear regression
Status:Individual
Hurdle:
Weighting:5%
Word limit:
Due date: Monday of Teaching week 11
____Australia：MCD2080: Business Statistics代写_______________________________________________________

This assignment is designed to test Unit Objective 4

This assignment is marked out of 30 and is worth 5% of the assessment in this unit. You must use Excel to generate the relevant output. The data for this assignment is in the file MCD2080_A2_T313.xlsx. The file has two worksheets, labelled Data,and Results.
The file is arranged so that all the required results can be presented in the worksheet labelled Results. The appropriate places for graphs, comments and tables are set out in this worksheet, and you are required to hand in a printed copy of the Results worksheet only. It is recommended that you first create the graphs and tables in the data worksheets, and then copy them to the appropriate places in the Results worksheet.  In fact on some computers it is essential that you work in this way, as some networked computers have difficulty dealing with data analysis tools when data is selected from a different worksheet.
The assignment is to be handed in as a printout of the completed Results worksheet. Do not print out the data. The Results worksheet has been set up to make printing as easy as possible but it is your responsibility to ensure that all required information actually appears on the pages you hand in. Be sure to include your name and student ID in the appropriate cells near the top left corner of the Results worksheet.  Your work must be easy to read.For questions involving written comments, the size of the textboxes on the Results worksheet are a general indication of the length of comments required (based on 11-point font.)  It is however permissible to make some adjustment to the size and shape of the textboxes, especially when this is necessary to arrange the worksheet for printing. 
Question
The manager of an Italian restaurant is interested in the relationship between the daily revenue (in $) and the number of patrons dining at the restaurant during that day. The number of patrons dining at the restaurant and the revenueearned from that day (in $)for each day over a one month period aregiven in the Data spreadsheet of the fileMCD2080_A2_T313.xlsx.All graphs and comments for this question should be placed in the appropriately labelled spaces in the worksheet Results.
 
(a)    Produce a scatter plot of the data [Graph (a)].  The chart must have an appropriate title and labels. Also you should rescale the graph axes to most clearly display the data. Describe the relationship between the variables as shown in the scatterplot. Is the relationship probabilistic or deterministic? Answerin Textbox (a).
5 marks
(b)   Using the regression function in Excel, generate regression output for the data and place it where indicated in the Results worksheet. As a check that you have conducted the regression correctly, make sure that the standard error (fourth number in the output) is equal to 222.1438.
                                 i.            Write down the line of best fit for the given data from the regression output obtained.  Clearly indicate the variables used in the equation in Textbox (b).
                               ii.            State the value of interceptof the equation correct to two decimal places in Textbox (b). Give aninterpretation and discuss the validity of this value.
                              iii.            State the value of the slope of the equation correct to three decimal places and give an economic interpretation of this valuein Textbox (b).
9 marks
 
(c)    Predict the revenue earned at the restaurant when the number of patrons dining at the restaurant for the day is:
                                 i.            296
                               ii.            357
         Comment on the reliability of each prediction answering in Textbox(c).
5 marks

4. State the coefficient of determination from the regression output. Explain what information the coefficient of determination gives about the relationship between the variables inTextbox (d).       

3 marks
 

5. State the coefficient of correlation from the regression output to three decimal places. Explain what information the coefficient of correlation gives about the relationship between the variables inTextbox (e).       

2 marks
 
(f)     Investigate whether the data provides statistical evidence of a linear relationship between the revenue earnedat the restaurant and the number of patrons dining there each day. Answer in Textbox (f).
                                 i.            Give appropriatenull and alternative hypotheses. (You are not required to type Greek letters with subscripts. You may use words or symbols instead of Greek letters. For example, H₀ can be written as H_0, and β1 as beta_1, etc.)
                               ii.            State the appropriate p-value for this test from the regression output. If the significance level were 1%, would the null hypothesis be rejected? At what levels of significance will the null hypothesis be rejected?
                              iii.            Briefly explain what a rejection of the null hypothesis means in this case.
6 marks
 
 
Presentation: Deductions may be made for poor presentation. If your presentation is easy to read, you will avoid any deductions.  Ease of reading is assisted by appropriate font size, borders, colour choice and labelling in graphs, and some care in spelling, grammar and punctuation.Australia：MCD2080: Business Statistics代写