Highlights
Instructions:This assignment is to be web submitted. Your answers must be in a Word document, You can paste any Excel workings as required in the document. Make sure to put your name & student ID number in the filename of your saved file (i.e.YourName_StudentID.docx).
Please show your answers to a maximum of three decimal places and most of the marks will be for interpretation and presentation of the results.Please ensure that ALL the work you hand-in is your own work. You may discuss how to answer the questions with friends, but each of you MUST write up your own answers. Any work that is too similar will be reported to the Head of School.
Lotteries (such as Lotto in NZ) have become important sources of revenue for governments. Many people have criticised lotteries, however, referring to them as a tax on the poor and uneducated. In an examination of the issue, a random sample of 100 adults was asked how much they spend on lottery tickets and was interviewed about various socioeconomic variables. The purpose of this study is to test the four following beliefs:
(i) Relatively uneducated people spend more on lotteries than relatively educated people.
(ii) Older people buy more lottery tickets than younger people.
(iii) People with more children spend more on lotteries than people with fewer children.
(iv) Relatively poor people spend a greater proportion of their income on lotteries than relatively rich people.
Download the data set “Lotteries.xlsx” from Moodle. The variables in the data set are:
• Amount spent on lottery tickets as a percentage of total household income (LSpend).
• Number of years of education (Edu)
• Age
• Number of children (# child)
• Personal income (Inc in thousands of dollars)
(a) Outline the key statistics for each of the variables, by using the descriptive statistics function in Data Analysis in Excel. Briefly describe each variable by referring to 3 or 4 of the statistics presented in the table. (Hint: Present the table showing all the statistics identified in the 1st column and then paste in the relevant information for each variable).
(b) Use Excel to draw a separate scatter plot for each independent variable against the dependent variable (i.e. amount spent on lotteries as a % of total income LSpend). Include the linear trend line for each graph. Using only the information from the graphs, which independent variable appears to have the strongest linear relationship with proportion of total income spend on lotteries? Briefly discuss if any of the belief’s i) to iv) are confirmed by the plots?
(c) (i) Develop a simple regression for each of the independent variables against the dependent variable and summarise the results in the table below. Include the p-value underneath each coefficient.
(g) Suggest one other variable that you think could have an impact on the proportion of income spent on lotteries. This new variable needs to be quantitative not a qualitativedummy variable. Briefly explain how you think it may impact on the dependent variable without actually obtaining a new regression equation.
(h) Now suggest a relevant qualitative dummy variable. Justify your choice of dummy variable and explain how you expect it to be related to the dependent variable.
(i) Finally, are there any policy implications from your regression equations and suggest one potential method of reducing the proportion spent on lotteries.
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