Residuals and Correlation Coefficient Primer

Let's Talk About Residuals!

By Jordan Canterbury

Hey! I need you to read carefully!

I'll do my best to explain this concept, but you need to pay close attention to what the captions and diagrams are telling you.

Some Old Vocabulary:

Scatterplot (review)

A visual representaiton of bivariate data.

Some Old Vocabulary:

Line of Best Fit (review)

It's the line that most-closely follows the trajectory of a scatterplot

Also known as the "linear best fit model"

Some Old Vocabulary:

Predicted Value (review)

The y-value of an ordered pair that on the line of best fit.

It is what the model would expect to happen for a given input (x) value.

Some Old Vocabulary:

Observed Value (review)

Any of the actual data points related to the given input. This is what really happened, and not what the model predicts.

Some ✨NEW✨ Vocabulary:

Residual, e

A measure of how far "off" the predicted value (in red) is from the actual value (in blue).

In other words, it is the estimation error.

Some ✨NEW✨ Vocabulary:

Residual, e

Calculated by subtracting the actual (blue) minus the predicted (red)

• The larger the number is, the more "off" your model was from that value

Some ✨NEW✨ Vocabulary:

Residual, e

• If the value is positive, the observed value was higher than expected.

• If the value is negative, the observed value was lower than expected.

Some ✨NEW✨ Vocabulary:

Residual, e

Calculate by subtracting:

Actual – Predicted

Some ✨NEW✨ Vocabulary:

Residual, e

Desmos is so sweet, dude. It automatically calculates the residuals for you, AND it puts them in the table.

A real friend, that Desmos is.

Click the "plot" button and relax!

Multiple Choice

If the ACTUAL y-value is 30, but the PREDICTED y-value is 20, what is the residual?

• –10

• 10

• 25

• 50

Some Old Vocabulary:

Correlation (review)

Describes how closely the two variables are related. It can be positive or negative, and be strong or weak.
If the line of best fit would have a positive slope, the correlation is positive!

Some Old Vocabulary:

Correlation (review)

The more closely packed-in the data, the stronger the correlation is.

Some Old Vocabulary:

Correlation (review)

The more spaced out the data is, the weaker the correlation is.

Some ✨NEW✨ Vocabulary:

Correlation Coefficent (r)

When you create a line-of-best-fit, you'll see a pair of statistics called r and r²

The r-value is a measure of how well the line-of-best-fit actually fits the data!

Desmos reports the r-value by default!

Some ✨NEW✨ Vocabulary:

Correlation Coefficent (r)

The r-value can range from –1 to 1. The closer to either end of the range, the stronger the correlation!

Multiple Choice

Which of the following is MOST likely the correlation coefficient for the scatterplot?

• 1.5

• 0.8

• 0

• –0.5

Match

Match each scatterplot to the r-value that BEST describes it

r = 0.75

r = 1

r = 0

r = 0.25

r = –1

• r = 0.75

• r = 1

• r = 0

• r = 0.25

• r = –1

COOL! You're done with this Quizizz lesson!

Head back over to Canvas and click the DeltaMath link for some practice!