Math 1 · Unit 10 · Lesson 1

Scatter Plots and Correlation

Real data is messy: the points only come close to a line or a curve. A scatter plot shows two quantities for many cases, one dot each. Describe it by direction (positive or negative), form (line or curve), and strength (how tightly the points hug the shape). The correlation coefficient r packs direction and strength into one number from negative 1 to 1: the sign is the direction and the size is the strength. r only measures how well a line fits.

About 40 minutes Sign is direction, size is strength

The big idea

Real data is messy. It does not follow an exact rule the way a sequence does; the points only come close to a line or a curve. A scatter plot shows the data, one dot per case, and you describe it three ways: direction (positive when the quantities rise together, negative when one rises as the other falls), form (does it look like a line or a curve), and strength (how tightly the points hug that shape). The correlation coefficient r is one number from negative 1 to 1 that measures how closely the points fit a line. Its sign gives the direction and its size gives the strength: exactly 1 or negative 1 means every point is on a line, close to them is strong, and close to 0 is weak. Read the graphing window first, because it shows roughly the domain and range of the data. And remember that r only measures fit to a line, so a curve can fool it.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Real data is messy: read the picture firstIn Unit 9 every list followed an exact rule: a perfect common difference or a perfect common ratio. 3One number for direction and strength: rStrength and direction can be packed into one number. 4Match r to the plotSix scatter plots and six values of r. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with direction, form, and strength, the r number line, what r = 0.97 tells you, and the two-look matching habit. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Building Sequences from the Real WorldThe end of Unit 9. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.S-ID.8 (find and interpret the correlation coefficient as the strength and direction of a linear relationship), NC.M1.S-ID.6a (the graphing window as the domain and range of the data).