Q1 An important first step to the statistical analysis of data is to "get to know your data". The following tasks should contribute to this.
(a) To the right of the dataset construct a small table in which the first column lists the Olympic years cited in the dataset. In the adjacent column sum the total of 'points' awarded across all countries in each year. Present this table in your report. [HINT:- Look at help on the SUMIF function.]
(b) Complete the TOTPTS column using the VLOOKUP function on the table created in (a). For each row of the main table evaluate PSHARE as the ratio between POINTS for a country in a year to TOTPTS for all countries in that year.
(c) Repeat this process to evaluate shares of total population and shares of total GDP of competing countries. Prepare a table showing summary statistics of all three shares including correlations between them and use your results to write a summary statement regarding the validity of equation [1] in the reference.
(d) Take the LN of all three shares for each country in each year and consider whether any of these three variables so transformed might be Normally Distributed.
Q2 In the paper, Table 1 presents results for a 'Tobit' model. This involves advanced estimation procedures which are not included in our module. However, we here consider a simpler version of the same idea using a 'Logit' model. In this model the independent variables are the same as in the Tobit but the dependent variable is 'Log-odds ratio'. That is, denoting a_{i}_{t} = PSHARE for country i in year t then:-
Log-odds ratio = Y_{i}_{t} = Ln(a_{i}_{t} /( 1 - a_{i}_{t} ))
(a) On a clean sheet construct a table in which the first column contains values for a_{i}_{t} in the range [0.1, 0.9] and the second column contains the corresponding values for the log-odds ratio. Convert this table into an XY plot and present the image in your report. Use the image to explain why our dependent variable might be used in this form.
(b) Present a table analogous to Table 1 using this as dependent variable and write a short summary of your table by way of interpretation. The lower section of this table you can replace with statistics from your standard regression outputs which you wish to refer to in your summary. For this question do not use 'year dummies'.
(c) Why does the original Table 1 refer to 'year dummies'? Repeat your version of this table as in (a) adding 'year dummies' in the estimation and present a new table, with interpretation in the style of Table 1 [i.e. do not list the year effects that you obtain in the estimation.]
Q3 (a) In Table 2 of the article an expanded set of independent variables is listed. Using Model (III) as an example, explain why these variables have been added and express the reason in the form of a statistical null hypothesis that can be tested.
(b) Apply the relevant test for (a) and set out your conclusion regarding this null. [Note:- There is no need to replicate the rest of the table for this question.]
Q4 (a) Using our version of the model formulated as (IV) in Table 1 describe how you would investigate whether the countries that are described as 'planned' and 'soviet' have affect the data by inducing heteroskedasticity. [Note:- you do not need to apply a procedure.]
(b) In the same model (IV) of Table 1 reference is made to a test of the null of equality between the two slope coefficients. Apply an F-test of this null.
Q5 UK (country code 195) population in 2012 is expected to reach 63million. By 2008 UK's GDP had risen by a third of its 1996 value but is only expected to achieve a further 0.5% per year on average to 2012. What share of the points would you expect UK to obtain in that Olympic year? What factors might affect the reliability of your expectations?