ECON 0150 | Economic Data Analysis

The economist’s data analysis skillset.


Part 2.1 | Relationships Between Numerical Variables

Bivariate Relationships

Let’s summarize what we know about four datasets.

Bivariate Relationships

Let’s summarize what we know about four datasets.

> same means, same standard deviations, same correlation between x and y…

> are these datasets the same?

Bivariate Relationships

Are these the same datasets?




Lets take a look at the data in a Notebook!

# Visualize all four datasets
sns.relplot(anscombe, x='x', y='y', col='dataset')

Bivariate Relationships

Are these the same datasets?

> very different! summarizing variables isn’t enough

Bivariate Relationships

Summary statistics can hide important patterns



  • The same mean, variance, and correlation can describe very different data
  • Visualizing relationships between variables allows us a clearer understanding
  • Part 2 is about exploring relationships in this way

Bivariate Relationships in Cross-Section

Q. Is there a relationship between GDP and coffee production?

> maybe, but it’s hard to see

> lets use a two dimensional graph

Bivariate Relationships in Cross-Section

Q. Is there a relationship between GDP and coffee production?

> two dimensions is nice, but the points have no meaningful relationships

Bivariate Relationships in Cross-Section

Q. Is there a relationship between GDP and coffee production?

> a scatterplot effectively visualizes scross sectional data with two dimensions

Bivariate Relationships in Cross-Section

Which countries have a GDP above $2 trillion?

> look at the horizontal axis and select all that are greater than 2

Bivariate Relationships in Cross-Section

Which countries have a GDP above $2 trillion?

> look at the horizontal axis and select all that are greater than 2

Bivariate Relationships in Cross-Section

Which countries have a production above ½ billion kg?

> and we can use either axis

Bivariate Relationships in Cross-Section

Which countries have a production above ½ billion kg?

> and we can use either axis

Bivariate Relationships in Cross-Section

Which countries produce less coffee per dollar than Brazil?

> we can also compare BETWEEN data points

Bivariate Relationships in Cross-Section

Which countries produce less coffee per dollar than Brazil?

> we can also compare BETWEEN data points

Bivariate Relationships in Cross-Section

Which countries produce less coffee per dollar than Brazil?

> separating lines can help make comparisons between ratios

Bivariate Relationships in Cross-Section

Which countries produce less coffee per dollar than Brazil?

> separating lines can help make comparisons between ratios

Bivariate Relationships in Cross-Section

Which countries produce more coffee per dollar than Brazil?

> separating lines can help make comparisons between ratios

Bivariate Relationships in Cross-Section

Which countries produce more coffee per dollar than Brazil?

> separating lines can help make comparisons between ratios

Bivariate Relationships in Cross-Section

Do the GDPs of the upper or lower pair differ by a larger amount?

> use the differences on the horizontal axis to measure differences

Bivariate Relationships in Cross-Section

Which is larger: the ratio of GDPs of the upper or lower pair?

> this question is difficult to answer with this scale

Bivariate Relationships in Cross-Section

Which is larger: the ratio of GDPs of the upper or lower pair?

> a log scale makes RATIOS easier to visualize: each tick is 10x larger

Bivariate Relationships in Cross-Section

Which country produces the second highest output of coffee?

> a log scale also makes it easier to see SCALING

Bivariate Relationships in Cross-Section

Which country produces the second highest output of coffee?

> scaling the vertical axis in logs clarifies both small and large variation

Bivariate Relationships in Cross-Section

Linear vs Log Scale: Same data, different views

> log scales reveal patterns hidden by outliers in linear scale

Adding More Variables

So far we’ve encoded two variables using position


  • x-position → GDP
  • y-position → Coffee Production
  • What if we want to show a third variable?

Trivariate Relationships: Size

We can use SIZE to encode a third numerical variable

> our standard scatterplot with position encoding

Trivariate Relationships: Size

Each point’s SIZE now represents population

> larger bubbles = larger population

Trivariate Relationships: Size

Indonesia and Brazil stand out — large countries with high production

> we can now see three variables at once: GDP, production, AND population

Trivariate Relationships: Color

We can also use COLOR to encode a third numerical variable


  • A continuous color scale maps values to shades
  • Lighter → lower values, Darker → higher values
  • Works well when size would be hard to compare

Trivariate Relationships: Color

Each point’s COLOR now represents population

> darker points = larger population

Trivariate Relationships: Color

Color makes it easy to spot high-population countries

> Brazil, Indonesia, and Ethiopia stand out as darker points

Summary



  • Scatterplots show relationships between two numerical variables
  • Log scales help compare ratios and see variation across orders of magnitude
  • Size encoding adds a third numerical variable (bubble charts)
  • Color encoding adds a third numerical variable (continuous color scale)

Exercise 2.1 | Cross-Sectional Scatterplots

Visualizing GDP and Coffee Production Relationships

Was the relationship between coffee production and GDP different in 1980?

  • Data: Beans_GDP_1980.csv

Exercise 2.1 | Cross-Sectional Scatterplots

How does GDP relate to coffee production? 

# Log both x and y variables
gdp['log_GDP'] = np.log(gdp['GDP'])
gdp['log_prod'] = np.log(gdp['coffee_prod'])
# Plot the log variables
sns.scatterplot(gdp, x='log_GDP', y='log_prod')

Exercise 2.1 | Log Transformation

Alternative: use log scale without transforming 

# Use a log scale without transforming the variable
sns.scatterplot(gdp, x='GDP', y='coffee_prod')
plt.xscale('log')
plt.yscale('log')

Exercise 2.1 | Cross-Sectional Scatterplots

How does GDP relate to coffee production? 

# Encode population size as bubble size
sns.scatterplot(gdp, x='GDP', y='coffee_prod', size='population', sizes=(10,200))

Exercise 2.1 | Cross-Sectional Scatterplots

How does GDP relate to coffee production? 

# Encode population size as color
sns.scatterplot(gdp, x='GDP', y='coffee_prod', hue='population')

Bivariate Relationships: Timeseries

How do the two commodity prices relate to each other?

> difficult to tell because of the axis scale

Bivariate Relationships: Timeseries

How do the two commodity prices relate to each other?

Bivariate Relationships: Timeseries

In which years did oil and coffee prices move in opposite directions?

Bivariate Relationships: Timeseries

In which years did oil and coffee prices move in opposite directions?

Bivariate Relationships: Timeseries

But are the two prices positively or negatively related to each other?

> this is difficult to see with just a Multi-Lineplot…

Bivariate Relationships: Timeseries

But are the two prices positively or negatively related to each other?

> a Scatterplot can show the relationship between two variables through time

Bivariate Relationships: Timeseries

Does the price of oil determine the price of coffee?

> a Scatterplot can only show associations not causation :(

Exercise 2.1 | Timeseries Scatterplots

Visualizing Coffee Prices and Oil Prices

We’re going to use a scatterplot to visually examine the relationship between coffee prices and oil prices.

  • Data: Coffee_Oil.csv

Exercise 2.1 | Timeseries Scatterplots

Visualizing Coffee Prices and Oil Prices 

# Scatterplot
sns.scatterplot(prices, x='Coffee', y='Oil')