Question: Lotteries are important sources of revenue for governments and charities. Many people have criticized lotteries, however, as taxes on the poor and uneducated. To explore the issue, a sample of 100 adults were asked how much they spend on lottery tickets and a number of socio-economic variables were also recorded. The study was meant to test the following beliefs:

1. Relatively uneducated people spend more on lotteries that do educated people.
2. Older people spend more on lotteries than do younger people.
3. People with more children spend more that people with fewer children.
4. Relatively poor people spend a greater proportion of their income on lotteries that the better off.

The file Lottery.xls contains data for the 100 respondents on the amount spend on lottery tickets as a percentage of household income, number of years of education, age, number of children and personal income (in thousands of dollars).

1. Ignoring any co-linearity issues, develop a single multiple regression model relating lottery expenditures to all of the independent variables described above and test the four beliefs listed above at the 95% confidence level. What would be the appropriate conclusions from this analysis?
2. Now check the correlation matrix for this data. Describe any concerns this matrix raises regarding the usefulness of the independent variables and the relationships between them. Without actually creating a new model, describe which independent variables you would use to improve the quality of model compared to the full model used in part a).

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