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The games of the 28th Olympiad were held in Athens | Complete Solution
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The games of the 28th Olympiad were held in Athens, Greece, in the summer of 2004. The data file contains information about 131 of the participating nations, including the following variables.[1]


Medals    (Won at Athens Olympics)
Gross Domestic Product    ($ Billion)
Population    (Million)
Area    (Million Sq. Km.)
Infant Deaths    Per 1,000 Births
Inflation Rate    
Fertility Rate    
GDP Growth Rate    
Telephones    (Million)
The final medal count is perhaps somewhat misleading as a measure of national athletic excellence. For example, the United States won the most medals in absolute terms (Exhibit 1), but isn’t even among the top ten in terms of medals per capita (Exhibit 2).
Country    Gold    Silver    Bronze    Total
United States    35    39    29    103
Russia    27    27    38    92
China    32    17    14    63
Australia    17    16    16    49
Germany    14    16    18    48
Japan    16    9    12    37
France    11    9    13    33
Italy    10    11    11    32
South Korea    9    12    9    30
United Kingdom    9    9    12    30
Exhibit 1: Top Medal Counts, 2004 Athens Olympics

 

Country    Medals    Population    Medals/Million Citizens
Bahamas    2    297,477    6.72
Australia    49    19,731,984    2.48
Cuba    27    11,263,429    2.40
Estonia    3    1,408,556    2.13
Slovenia    4    1,935,677    2.07
Jamaica    5    2,695,867    1.85
Latvia    4    2,348,784    1.70
Hungary    17    10,045,407    1.69
Bulgaria    12    7,537,929    1.59
Greece    16    10,665,989    1.50
Exhibit 2: Top Medal Counts per Capita, 2004 Athens Olympics
 
Add a dummy variable to the data set, representing whether the nation was the host of the Olympics. (Hint: The 2004 Athens Olympic Games were hosted by Greece.) Perform a correlation analysis on all of the variables in the data set, and show the results here in descending order of importance.

 

[1] Some interesting countries, such as Russia and Jamaica, are excluded from the data set because information was not available for all variables.


1.   Add a dummy variable to the data set, representing whether the nation was the host of the Olympics. (Hint: The 2004 Athens Olympic Games were hosted by Greece.) Perform a correlation analysis on all of the variables in the data set, and show the results here in descending order of importance. Explain your results.

2.  Show scatter diagrams of the two most important predictors, showing their relationship to “Medals”. Use labels to indicate interesting outliers, show a linear trend line, and write something intelligent about your graphs.

3. Create a multiple regression model, based on your analysis above. Try to find the model that has the highest adjusted R-square value for predicting the number of Olympic medals won by a country.

4. Using your model from above, perform a hypothesis test to see whether the true effect of “Area” is less than one medal for every 1,000,000 square kilometers at the 5% level of significance, all other factors taken into account. Find the p-value of your test and explain its meaning.

5. Using your model from above, and assuming the same test, alpha, and variance as in Part 10, what would be the risk of a Type II error if the true effect of “Area” were in fact known to be 0.5 medals per 1,000,000 square kilometers?


6. Using your model from Part 9 above, calculate the residual error in “Medals” for each country. Show the residual errors for the ten countries who most “overperformed” in the Athens Olympics (i.e. won more medals than your model predicted they would) and the ten countries who most “underperformed”. Explain your results.


7. Discuss the residual errors in this model. Use charts as appropriate.


8. Do these data provide evidence of a “home field advantage” in the Olympics? In other words, can we conclude that Greece won medals above and beyond what would otherwise been expected because it was the host country?

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The games of the 28th Olympiad were held in Athens | Complete Solution
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From the above two graphs we see that the r-square values are almost same hence the relation is equally stro...
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