9th grade · Math · Unit 22 of 22
The Correlation Coefficient
What r tells you
What your child practices
Reading the correlation coefficient r that technology gives for a line of best fit: its sign shows direction, its closeness to 1 or −1 shows strength, and it never shows cause on its own.
New York State Learning Standards learning standard: AI-S.ID.8 · calculating the correlation coefficient of a linear fit with technology and interpreting it
How we explain it
Children can open this short lesson before they practice.
- The correlation coefficient r, found with technology, is between −1 and 1.
- Its sign gives the direction; closeness to 1 or −1 gives the strength of the linear pattern.
- r near 0 means little linear relationship. A strong r never proves cause.
Example: r = −0.91 for a car's age and its value. What does it mean? The sign is negative: value tends to fall as age rises. 0.91 is close to 1: the points lie close to a line. Answer: A strong negative correlation
The Correlation Coefficient in New York
In the New York State Learning Standards, this is unit 22 of 22 in 9th grade Math, after Units & Accuracy.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
For outdoor temperature (x) and heating bill (y), r = −0.27. What does this tell you?
- 27% of the points are on the line
- higher outdoor temperature tends to go with higher heating bill
- higher outdoor temperature tends to go with lower heating bill, but the points are widely scattered
- outdoor temperature causes the change in heating bill
higher outdoor temperature tends to go with lower heating bill, but the points are widely scattered
Hint: r tells the direction and strength of a linear pattern. It never shows cause on its own.
Question 2
A scatter plot curves like a U, and r is close to 0. What does this tell you?
- there is no linear relationship, though there may be a curved one
- the relationship is strongly linear
- the data is wrong
- there is no relationship of any kind
there is no linear relationship, though there may be a curved one
Hint: r only measures linear patterns.
Question 3
Technology gives a correlation coefficient of r = 0.22. How would you describe it?
- weak negative correlation
- almost no linear correlation
- weak positive correlation
- strong negative correlation
weak positive correlation
Hint: The sign gives the direction. Close to 1 or −1 is strong; close to 0 means little or no linear relationship.
Question 4
Which correlation coefficient shows the strongest linear relationship?
- r = 0.92
- r = −0.03
- r = 0.31
- r = −0.32
r = 0.92
Hint: Strength depends on how close r is to 1 or −1, not on its sign.
Question 5
Technology gives a correlation coefficient of r = −0.32. How would you describe it?
- strong positive correlation
- weak negative correlation
- strong negative correlation
- almost no linear correlation
weak negative correlation
Hint: The sign gives the direction. Close to 1 or −1 is strong; close to 0 means little or no linear relationship.
Question 6
For hours of practice (x) and free throws made (y), r = 0.98. What does this tell you?
- higher hours of practice tends to go with higher free throws made, and the points lie close to a line
- hours of practice causes the change in free throws made
- 98% of the points are on the line
- higher hours of practice tends to go with lower free throws made
higher hours of practice tends to go with higher free throws made, and the points lie close to a line
Hint: r tells the direction and strength of a linear pattern. It never shows cause on its own.