MAE256 Data Analysis of Olympic Data - Regression Analysis Assignment Solution

• Descriptive Statistics

The descriptive statistics of the Real GDP, Population and Total Medals can be found in the table above. It is apparent that on average $137727 million dollars is the Real GDP of countries that have won Olympics. The minimum Real GDP value is $46 million dollars while the maximum Real GDP is $7280000 million dollars. The standard deviation and variance are used for measuring the dispersion in the data while range shows the difference between highest and lowest value (Leech, Barrett, & Morgan, 2013). The standard deviation of $548622 million dollars shows that the Real GDP on average is $548622 away from the mean. A large standard deviation means that the values in the data set are farther away from the mean, on average. 

The highest population in millions in countries is 1220 million while the lowest population number is 0.015 million. On average 27.53 million people are living in the countries that have won Olympic game. The standard deviation of 93 million shows that the population on average is 93 million away from the mean. There are on average 5 total medals (sum of gold, bronze and silver) won by the countries in data set. Maximum medals won are 195 by a country while minimum medals are 0.  The standard deviation shows that on average total medals won deviates from the mean by 16 medals. 

The kurtosis value for all three variables is positive showing that the data is positively (right) skewed (Morgan, 2000). The higher values for all three variables indicate that the data points are extremely skewed to right. The skewness values are also positive showing that the data points are positively skewed. 

• Simple Regression Model 

For calculating the simple regression model, total medals are taken as dependent and real GDP is taken as independent variable. 

TotalMedals=β0+ β1realGDP+u

The model summary shows that 41.5% variation in total medals won is explained by the real GDP of country. This shows a weak model fit as the independent variable chosen is not effectively explaining the variation in total medals won.

The above table shows the values of constant and betas. The regression line is given as:

TotalMedals=2.458 + 0.00001900 GDP+u

β0 = It is a constant term meaning that in absence of Real GDP, the countries still have approximately 3 medals (including gold, bronze and silver).