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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 isnt
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?

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
DeathsPer
1,000 BirthsInflation
RateFertility
RateGDP
Growth RateTelephones(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 isnt
even among the top ten in terms of medals per capita (Exhibit 2).CountryGoldSilverBronzeTotalUnited States353929103Russia27273892China32171463Australia17161649Germany14161848Japan1691237France1191333Italy10111132South Korea912930United Kingdom991230Exhibit 1: Top Medal Counts, 2004
Athens OlympicsCountryMedalsPopulationMedals/Million CitizensBahamas2297,4776.72Australia4919,731,9842.48Cuba2711,263,4292.40Estonia31,408,5562.13Slovenia41,935,6772.07Jamaica52,695,8671.85Latvia42,348,7841.70Hungary1710,045,4071.69Bulgaria127,537,9291.59Greece1610,665,9891.50Exhibit 2: Top Medal Counts per
Capita, 2004 Athens OlympicsAdd 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?”