Big Bang Data

Let’s devote this post to summarize what we have done so far and what our conclusions are. As you might know by now we are working with the Gapminder data set and my research questions read:

Is there an association between life expectancy (response variable) and employment rate (explanatory variable)? 

Does the variable CO2 emissions play a role in affecting this relationship?

My hypothesis: I believed that both variables will affect the life expectancy in a positive direction, meaning keeping either of the variable fixed and increasing the other would lead to and increase in life expectancy.

After removing rows with incomplete observations we can visualize all three variables in a histogram.

The variable with CO2 emissions is extremely right skewed and has very high variability. This is addressed by creating a new variable called log_co2 where we have taken the natural logarithm of the original variable. The employment rate variable has a std. around 20 and is a bit right skewed while the life expectancy variable is a bit left skewed with a std. of around 10. The histogram of log_co2 can be viewed below.

The variability is now much lower with a std. of 5. 

In order to examine the first research question we plot employment rate and life expectancy in a scatter plot.

Unfortunately this does not make us any wiser. There actually seems to be no correlation at all between the variables. This can also be confirmed by grouping the employment rate according to the categories below and the use a bar plot for visualization.

if (employrate le 51.2) then employ_level = 1; else if (employrate le 58.8) then employ_level = 2; else if (employrate le 65) then employ_level = 3; else employ_level = 4;

We might want to color code the CO2 emission and try to get some more insight.

As it is quite hard to discern any patterns in this we opt for another strategy where we creates levels of CO2 emissions:

if (10 <= log_co2 <= 18.5)then co2_level = 1; else if (18.5 < log_co2 <= 21.2) then co2_level = 2; else if (log_co2 > 21.2) then co2_level = 3;

The interesting thing here is that as a stand alone variable employment rate does not seem to give information about life expectancy but together with CO2 there actually seems to be some interesting relations as can be seen below:

First we have a look at the distribution of CO2 emissions:

proc sgplot data = mydata.gapminder; histogram co2emissions; * has a nasty skew; run;

It is immediately observed that the distribution has a really nasty skew. To sort this out I create a new variable called co2_log that is the natural logarithm of the co2emissions variable above. 

data gapminder2; set mydata.gapminder; log_co2 = log(co2emissions); proc sgplot; histogram log_co2; * looks really nice; run;

This looks way better. The distribution seems normal like and the range of the distribution has now diminished significantly. I now create a new categorical variable called co2_level. 

data gapminder2; set gapminder2; if (10 <= log_co2 <= 18)then co2_level = 1; else if (18 < log_co2 <= 20.5) then co2_level = 2; else if (log_co2 > 20.5) then co2_level = 3; else if missing(log_co2) then co2_level = .; proc freq; tables co2_level; run;

As we can can this variable has three levels: 1, 2 and 3. And the higher the level the higher the CO2 emissions of that country. From proc freq we see that the groups are similar in size.

In addition we have 13 missing values. Observations where we have missing values are removed:

proc print data = gapminder2 (obs = 10); var country co2emissions log_co2 co2_level; proc sort; by log_co2; run;

* Delete observations with missing values; data gapminder2; set gapminder2; keep country lifeexpectancy employrate co2emissions log_co2 co2_level; if cmiss(of lifeexpectancy employrate co2emissions log_co2 co2_level) then delete; run;

After removing observations with incomplete information we print the 10 first rows of our data set and check the co2_level variable.

proc print data = gapminder2 (obs = 10); proc freq; tables co2_level; run;

The categories are a bit uneven (see cumulative percent where our aim is to get equally sized categories that is 33.3, 66.7 and 100 %). Redefining the categories as below gives more equally sized groups. 

data gapminder2; set gapminder2; if (10 <= log_co2 <= 18.5)then co2_level = 1; else if (18.5 < log_co2 <= 21.2) then co2_level = 2; else if (log_co2 > 21.2) then co2_level = 3; else if missing(log_co2) then co2_level = .; proc freq; tables co2_level; run;

The final step is to return to the plot where we finished off last time. Now when we have our co2_level categories we can color code these and see more clearly how CO2 emissions, employment rate and life expectancy are associated. 

The next step is to use SAS for exploring the data set. I want to show how to use the frequency procedure in SAS for counting categorical variables and creating bar plots. Somewhat unfortunate the data set does not contain any categorical variables. To alleviate this I choose to view the democracy score as categorical. Above we see that countries with a low democracy score also seem to engage a greater percentage of the population in the armed forces. This makes somewhat sense since less power to the people would probably lead to an increased riot risk.

Moving on to my research question: Is there any association between employment rate, CO2 emissions and life expectancy. Below I have created a bubble plot to illustrate the data. 

At first sight my hypothesis that high CO2 and employment rate would lead to a higher life expectancy seems a bit unclear. There does not seem to be a clear correlation at all. This calls for further investigation...

My SAS code is shown below:

%macro barplot(logic_operator, value); data gapminder; set mydata.gapminder; label polityscore="2009 Democracy Score (Polity)" armedforcesrate="Armed forces personnel (% of total labor force)"; where (polityscore &logic_operator &value);

proc sort ; by country;

proc freq ; tables polityscore;

proc sgplot ; vbar polityscore / response=armedforcesrate name="Bar" stat=Mean; yaxis grid; title "Mean of armed forces rate"; run;

%mend;

%barplot(>, 0); %barplot(<=, 0);

/*--Set output size--*/ ods graphics / reset width=6.3in height=4.8in imagemap; * Investigation of my research question: Is there any association between the variables life expectancy, CO2 emission and employment rate?;

/*--SGPLOT proc statement--*/ proc sgplot data=mydata.gapminder; /*--TITLE and FOOTNOTE--*/ title 'Life expectancy against employment rate with CO2 information'; footnote2 j=l 'The larger the bubble the larger the CO2 emission of that country.';

/*--Bubble plot settings--*/ bubble x=employrate y=lifeexpectancy size=co2emissions/ fillattrs=(color=CX3ec439 transparency=0.4) dataskin=crisp name='Bubble';

/*--X Axis--*/ xaxis grid;

/*--Y Axis--*/ yaxis grid; run;

I have chosen to work with the GapMinder data set. My research question is: 

Is there an association between CO2 emission, employ rate and life expectancy?

Quite natural we already expect that there of course will be an association between these variables and as such my goal of the project is more targeted against learning how to use SAS as a tool for answering the question.

Hi everyone,

This is my first course at Coursera and I will be sharing my work and experiences here on tumblr. First out is the course Data Management and Visualization which is part of the Data Analysis and Interpretation Specialization.

The course consists of four assignments that should be completed using SAS or Python. The results of each assignment will be shared on this blog. I hope you’ll enjoy following my journey to becoming a data analysis expert.