Visualizing Relationships

Statistics 4868/6610 Data Visualization

Prof. Eric A. Suess

2/22/2016

Today we will go over what correlation measures and some of the examples from Chapter 6.

The plots from Chapter 6

• Scatterplot
• Scatterplot Matrix
• Correlogram
• Bubble Chart

In introductory Statististics courses the difference between Correlation and Causation is discussed. These two ideas are not the same.

Often it is said, “Correlation is not causation.”

The Correlation Coeficient, \( r \), measures the strength and direction of the linear association between two quantitative variables.

Memorize this!

Good interview question.

One variable causes an effect, linear or non-linear, on another another variable.

Causality

Probabilistic Causation

A confounding variable is another variable that influences the other variables.

Simpson's Paradox

Edward Simpson: Bayes at Bletchley Park

### synthetic data

# Consider book price (y) by number of pages (x)

z = c("hardcover","hardcover",
      "hardcover","hardcover",
      "paperback", "paperback","paperback", 
      "paperback")

x1 = c( 150, 225, 342, 185)
y1 = c( 27.43, 48.76, 50.25, 32.01 )

x2 = c( 475, 834, 1020, 790)
y2 = c( 10.00, 15.73, 20.00, 17.89 )

x = c(x1, x2)
y = c(y1, y2)

# correlation

cor(y, x)

[1] -0.5949366

cor(y1, x1)

[1] 0.8481439

cor(y2, x2)

[1] 0.9559518

# linear regression

lm(y ~ x)

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
   41.15238     -0.02665  

# linear regression

lm(y1 ~ x1)

Call:
lm(formula = y1 ~ x1)

Coefficients:
(Intercept)           x1  
    13.0613       0.1177  

# linear regression

lm(y2 ~ x2)

Call:
lm(formula = y2 ~ x2)

Coefficients:
(Intercept)           x2  
    1.72389      0.01819  

Summary: Simpson's Paradox is the changing of the direction of a relationship with the introduction of another variable.

The relationship between Price and Number of pages in a book changes with the introduction of the variable Type of Book (Hardcover, Paperback).

See the R Markdown document SimpsonsParadox available on RPubs.com/esuess.

The Scatterplot matix is a very useful plot for seeing the correlations between variables in a dataset.

Not so useful with more than about 10 variables.

What to do with more variables?

From the Quick-R website.

Correlogram

library(corrgram)

Be sure to study the discussion of the use area in the section about Bubbles on pages 193 and 194. Look at Figure 6-12, 6-13, 6-14, 6-16 and 6-17. Study Figure 6-17 that uses the correct sized cirles.