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# Regression analysis for data on lettery, education, age, children

See attached data file.

3. Attached you will find the excel data and analysis on the topic of 'playing the lottery'. It is often claimed that individuals who play the lottery are those who can least afford to do so, making the impact of the lottery 'regressive'. In this context, regressive implies that lower income individuals play the lottery more than do higher income individuals.

The data for this analysis include 100 randomly chosen men from a major metropolitan area. For each individual, the following information has been recorded:

- The number of times in the preceding month the individual has played a state-sponsored lottery. This is the dependent variable in the accompanying regression analysis.

- The education of the individual, measured by the number of years of schooling completed. Note that 12 years of schooling completed means that the person has graduated from â??high schoolâ?, and 16 years of schooling completed means that the person has graduated from college.

- Age in years at the person's most recent birthday.
- The number of children currently living in the person's household.
- The person's annual 'wage and salary' income in the previous year, in thousands of dollars.

The output includes a listing of all 100 observations; descriptive statistics for each variable; and, the results of a regression analysis that uses lottery as the dependent variable, and education, age, number of children, and income as independent variables. Each of these outputs is on a separate worksheet.

a. Write out the regression equation, with specific intercept and slope estimates. That is, I want the estimated numerical values of the intercept and the slopes in the equation you write.

b. For the first row of actual data from the excel file, use the independent variable values to â??predictâ? the value of the dependent variable. For this row, also compute the 'residual' (actual value of lottery play minus the predicted value).

c. For the independent variables 'Age' and 'Income' interpret the numerical value of the estimated slope, which you can obtain from the excel regression output.

d. Evaluate the statistical significance of each of the four slope estimates. This can be done in a very summary way. Start out by indicating the 'null value' against which you will be testing each of the four slope estimates. Then, next to the name of each independent variable, state whether the slope is 'significant', and why. The 'why' should be stated in no more than a few words or a single sentence. Use a significance level of 0.05.

e. For the independent variable 'Income', interpret the p-value of the estimated slope, briefly and specifically (by specifically I mean with specific reference to the numerical value of the p-value as reported on the excel regression output).

f. Is the main argument made in the preamble to this question supported by the research? Explain why or why not, in a sentence or two.

g. Use the R-square and the standard error of the estimate to evaluate the overall reliability of the regression.

#### Solution Preview

Regression analysis
3. Attached you will find the excel data and analysis on the topic of playing the lottery. It is often claimed that individuals who play the lottery are those who can least afford to do so, making the impact of the lottery regressive. In this context, regressive implies that lower income individuals play the lottery more than do higher income individuals.

The data for this analysis include 100 randomly chosen men from a major metropolitan area. For each individual, the following information has been recorded:

â€¢ The number of times in the preceding month the individual has played a state-sponsored lottery. This is the dependent variable in the accompanying regression analysis.
â€¢ The education of the individual, measured by the number of years of schooling completed. Note that 12 years of schooling completed means that the person has graduated from high school, and 16 years of schooling completed means that the person has graduated from college.
â€¢ Age in years at the personals most recent birthday.
â€¢ The number of children currently living in the personal household.
â€¢ The personal annual wage and salary income in the previous year, in thousands of dollars.

The output includes a listing of all 100 observations; descriptive statistics for each variable; and, the results of a regression analysis that uses lottery as the dependent variable, and education, age, number of children, and income as independent variables. Each of these outputs is on a separate worksheet.

a. Write out the regression equation, with specific intercept and slope estimates. That is, I want the estimated numerical values of the intercept and the slopes in ...

#### Solution Summary

A regression analysis for data lettery, education, age and children are examined.

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