Lecture 2.1 - Association and correlation

Association and correlation

Exercise 1

In your pairs, try to think of two variables that, in the real world, that might have this correlation for each of the following correlations. Try to think of a few examples for each correlation.

• 0.75
• 0.25
• 0.0
• -0.25
• -0.75

Pick a few of these and draw by hand what you expect these graphs to look like.

Exercise 2 - Art

Viewing an example relationship

• First, what is our expectation about the relationship between height (cm) and width (cm) of paintings sold recently at Sotheby’s?
• Direction?
• Form?
• Strength?
• Outliers?

Which variable should be the response variable? Why?

Height and width - direction

A scatterplot is the easiest way to check for direction. In this case, the direction is obvious

Height and width - form

Height and width - strength

Correlation as a measure of strength

This correlation is perhaps what we expected

• In general, mechanically generated processes with little noise can have very high correlations
• Most correlations of social or real world processes rarely have above moderate correlation due to noise

Height and width - outlier

Again, we do not have a rule for selecting outliers other than to observe them on the scatterplot. In this case, there is one very obvious value far from other values

To investigate if these outliers matters, we can check some other values of the observation.

What kind of outliers do you think these are? Why?

Outliers - actual observations

Beneath the Sun

Yellow and Orange Orchid Clipping

https://www.sothebys.com/en/buy/auction/2021/contemporary-showcase-kawaii-pop/yellow-and-orange-orchid-clipping-huang-ju-se-lan

Data with no outlier

How much do you think the correlation will change?

Describing the association

1. Direction - positive
2. Form - linear
3. Strength - strong
4. Outliers - one(ish)? possible

Outlier:

Does bed and square feet relationship match expectations?

• Not surprisingly, the higher the painting, the wider it (usually) is (positive relationship)
• The relationship is fairly linear (form is lineaer)
• Most points are relatively “clustered” indicating a strong relationship (relationship is strong)
• Outlier analysis leads to some potential issues

Your turn

With your partner, develop some expectations about whether the variable area_cm2 and price in the art dataset might be related.

What to do with your partner:

1. Write down what you expect the relationship to be between these two variables based on any prior knowledge
2. Decide which variable is the response variable and which is the predictor variable
3. Make a scatterplot using one of the codeblocks in the previous section and identify the features of the association