Question: 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)

a) 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.

b) 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).

c) 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).

d) 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.

e) How might you improve on the above model and results?