The Task

Carry out appropriate analyses using SPSS and produce a report on all of the following three tasks. The main body of the typed report should not exceed 8 sides of A4 (use 11 point font or larger, and \(1 \frac{1}{2}\) spacing, and include margins, and should include descriptive and/or test statistics, \(p\) -values where appropriate, your conclusions and full interpretation of the results. In addition, relevant computer output should be included in an appendix (no more than 7 pages in total). Make sure that you follow all ground rules for a good report mainly presentation of data in tabular formats and interpretation of results. Keep your answers short and to the point.

The Data

The data for this assignment are stored in the SPSS file, which can be downloaded from Blackboard (folder 'Assignment' of this module). This data file includes six rounds of the ONS Omnibus survey module focusing on charitable giving which were conducted during the years 2004 to 2007 . It includes information on whether a person donated to charities and the amount donors donated as well as individuals' socio-economic background (gender, marital status, education etc.). Look at the description of the variables that can be obtained from the Variable View sheet once you have loaded the data into SPSS. In addition, see the following additional information on four variables in the data set:

Task 1

1. Answer the following questions:

1. What is the percentage of females who donate to charities and what is the percentage of males donating to charities?
2. Of those who donate to charities, what percentage of respondents is married?

2. Carry out an appropriate test for association of income (use the variable 'quintile') and donor status. State the null and alternative hypotheses and give your conclusions from the result of the test.

3. Produce and interpret summary statistics and \(95 \%\) confidence intervals of the mean amount donated for donors only

1. with high income;
2. without high income.

(Note: use the variable 'highincome' for a and b.) Comment on any differences/similarities between the groups.

4. Using a \(1 \%\) significance level, test for a difference in the amount of money donated by female and male donors. In each case state the null and alternative hypotheses and your conclusions based on the result of the test.

Task 2

For this task, we want to examine in greater detail who donates to charities. Hence, we will focus on whether someone is a donor or not (variable 'donor'). (How much someone donates is not of importance for this task.)

In detail, we want to examine the following research question: what is the impact of the following combination of individuals' characteristics on the probability of being a donor: individuals' gender (variable 'female'), their income ('highincome'), their education

('degree'), their age ('respage') and whether they have a professional occupation

('oce prof').

1. Run one single regression model that makes it possible to examine this research question taking all the variables stated in the research question given above into account. (You do not need to take interaction terms into account.)
2. Interpret the model fit and discuss the size and the significance of the regression coefficients.
3. Calculate the predicted probability of being a donor for i) a 40 year old woman with high income, degree education and professional occupation and ii) an 80 year old man, with low income, not professional occupation and low education. Show how you derived at your results in detail.

Task 3

In the following we want to examine whether age and gender are important variables for explaining the amount donated to charities by donors conditional on other individuals' socioeconomic background factors. For the whole analysis in Task 3 focus only on people who are donors.

1. In the context of this research question, explain what 'conditional' means and discuss why this might be of interest.
2. Run one regression model in which the amount donated ('amount') is the dependent variable and age ('respage') is the explanatory variable.

1. Write down the regression equation.
2. Interpret the regression coefficient of the explanatory variable.
3. Do a formal test to examine whether the regression coefficient is significant. Interpret your result and explain why a significant test is needed.
4. Given your regression equation, what is the predicted amount donated in £ of a person being 50 years old.
5. Check for the Normality Assumption by creating a histogram of the standardised regression residuals and a Normal P-P Plot and discuss your results.
6. Create a new variable called 'lnamount' which gives the natural logarithm of the variable 'amount' (create this variable only for those people who are donors). Provide a summary statistic of this newly created variable and the old variable 'amount' and discuss differences of the distribution of both variables.

3. For the following regression analysis conducted in this sub-section 3 , we will use the newly created variable 'lnamount' as dependent variable. Run two separate regression models. For Model 1, the variable 'lnamount' is the response and gender ('female') is the independent variable. For Model 2 , add the following independent variables to Model 1: age ('respage'), education ('degree'), income ('highincome'), an interaction variable between age and highincome.

1. Explain why we choose now 'lnamount' instead of 'amount' as dependent variable.
2. Present the results of the both regression models in one single table that first includes all the important information for interpreting the results, second is clear and third makes it possible to compare regression coefficients between the both models easily.
3. Using results of Model 2 only, interpret the regression results by discussing the impact and significance of all the explanatory variables on the amount given to charities.
4. Explain what the interaction variable tests and discuss the result.
5. Using Model 2 only, state the predicted regression equation for people with high income and low income separately.
6. Using your result of 3 e), predict the amount given in $£$ for i) a 50 year old male with high income and degree and ii) a 50 year old female with low income and low education.
7. Compare significance and value of the coefficient of the variable 'female' between Model 1 and 2. Try to explain the result.
8. Compare briefly differences in the model fit between both models.

Price: $32.06

Solution: The downloadable solution consists of 12 pages, 2006 words and 14 charts.
Deliverable: Word Document