1. Consider the following data on the annual rate of growth of Gross Domestic Product (GDP) for a sample of countries, in 2010:

1. Derive the mean, mode, range, variance and standard deviation for the above sample of countries.
2. Discuss the strengths and weaknesses of each of the statistical measures you have derived in part (a) of this question and interpret them in the context of this dataset.

2. A researcher wishes to test the hypothesis that output per employee (Y/L) is related to investment per employee (I/L) and has attained the following data for 10 companies. Answer all parts of this question:

1. Show how the researcher should set out the null hypothesis and the alternative hypothesis.
2. Calculate Pearson’s correlation coefficient for output per employee (Y/L) and investment per employee (I/L).
3. Using the t-statistic for Pearson’s correlation coefficient comment on the degree of statistical significance of the correlation coefficient attained in part (b).
4. On the basis of your results what advice would you give to companies that wished to increase output per employee?

3. Answer all parts of this question.

A business analyst has observed the distribution of growth rates across all countries and noted that growth rates are normally distributed with a mean of 6.5 and a standard deviation of 1.6.

1. Explain how any variable that is normally distributed may be transformed into one that follows the standard normal distribution.
2. Calculate the probability that a country’s growth rate exceeds 10 per cent.
3. Calculate the probability that a country’s growth rate is less than 4 per cent.

4. Answer all parts of this question.

A researcher has the following data for growth rates and investment as a percentage of Gross Domestic Product (GDP) in 2010:

Table 3 Annual Percentage Growth Rates in GDP and Investment as a Percentage of GDP, 2010 (Source: World Bank)

1. The relationship between growth (g) and investment as a percentage of GDP (I/Y) is assumed to be given by the following linear model:
   \[{{g}_{i}}={{\beta }_{1}}+{{\beta }_{2}}{{\left( I/Y \right)}_{i}}+{{u}_{i}}\]
   Set out a null and an alternative hypothesis for β1 and β2. Calculate estimates of β1 and β2 using Ordinary Least Squares (OLS) regression. Show your calculations in a table with clear headings. Presentation is important.
2. Consider the estimate of the constant term β1 and discuss whether it is significant and meaningful. (To test the significance you need to conduct a t-test, you may use SPSS to attain the t-statistic but you must set out the test clearly in relation to the hypotheses you’ve specified in part (a) above).
3. Consider the estimate of the slope coefficient β2 and discuss its size, sign, significance and meaning. (To test the significance you need to conduct a t-test, you may use SPSS to attain the t-statistic but you must set out the test clearly in relation to the hypotheses you’ve specified in part (a) above).
4. Use SPSS to calculate R2 and R2 adjusted. Explain the meaning of the R2 statistics and comment on their size. What is the advantage of using R2 adjusted rather than R2? Perform an F-test and comment on the overall significance of the regression.
5. How might you improve on the above model and results?

Section 3

5. Examine the factors determining hourly wages using the dataset on wages provided on Moodle (this is the dataset you have been using in the labs). Your answer should contain a discussion of theories of wage determination e.g. theories of human capital, theories of discrimination and so on. Set out the hypotheses you are testing and the models you plan to estimate using regression analysis. Comment on the size, sign and significance of the regression coefficients (β’s). Carry out diagnostic tests and discuss possible problems, such as multicollinearity, heteroscedasticity, autocorrelation, simultaneous equations bias and the limitations of your results. Present your results clearly in tables and provide a full discussion that explains your findings clearly to the reader.

Data: the data are available on Moodle and are from Dougherty’s dataset.

Literature: there is a vast literature on the determinants of wages across individuals. Carry out a literature search using the Social Science Citation Index to locate relevant literature (Web of Knowledge database). Much will depend on your findings from this search as it will provide the basis and rationale for the hypotheses you wish to test and the models you estimate. You should also discuss your results in the context of previous results and findings published in the literature.

Write-up your results clearly and carefully. Please do not simply cut and paste output from SPSS – look at how the results are presented in the article by Chang and Wong (2004) and follow that style of presentation. Note that results that reject hypotheses are just as valuable as results that confirm hypotheses. The key thing is to write up your results as clearly and impartially as possible using your knowledge of quantitative methods and regression analysis.

Price: $38.8

Solution: The downloadable solution consists of 22 pages, 1680 words and 24 charts.
Deliverable: Word Document