Worksheets · Statistics

Correlation coefficient worksheet

r runs from −1 to 1: its sign gives the direction and its size the strength of a straight-line relationship. Squaring it gives the share of the variation in y that the line explains.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Correlation Coefficient

Date Period

Answer each question.

  1. For a set of data, r=−0.55. What percent of the variation in y is explained by the linear relationship with x?
  2. Describe the direction and strength of a linear relationship with r=0.45
  3. For a set of data, r=−0.3. What percent of the variation in y is explained by the linear relationship with x?
  4. Describe the direction and strength of a linear relationship with r=−0.55
  5. Describe the direction and strength of a linear relationship with r=−0.1
  6. For a set of data, r=−0.1. What percent of the variation in y is explained by the linear relationship with x?
  7. For a set of data, r=−0.85. What percent of the variation in y is explained by the linear relationship with x?
  8. For a set of data, r=0.6. What percent of the variation in y is explained by the linear relationship with x?
  9. Describe the direction and strength of a linear relationship with r=0.7
  10. For a set of data, r=−0.4. What percent of the variation in y is explained by the linear relationship with x?
  11. For a set of data, r=0.95. What percent of the variation in y is explained by the linear relationship with x?
  12. For a set of data, r=−0.75. What percent of the variation in y is explained by the linear relationship with x?
  13. For a set of data, r=0.2. What percent of the variation in y is explained by the linear relationship with x?
  14. Describe the direction and strength of a linear relationship with r=−0.75
  15. Describe the direction and strength of a linear relationship with r=0.6
  16. For a set of data, r=0.7. What percent of the variation in y is explained by the linear relationship with x?
  17. Describe the direction and strength of a linear relationship with r=−0.85
  18. For a set of data, r=0.45. What percent of the variation in y is explained by the linear relationship with x?
  19. Describe the direction and strength of a linear relationship with r=−0.4
  20. Describe the direction and strength of a linear relationship with r=−0.3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Correlation CoefficientAnswer keyVersion 1

Date Period

Answer each question.

  1. For a set of data, r=−0.55. What percent of the variation in y is explained by the linear relationship with x?30.25%
  2. Describe the direction and strength of a linear relationship with r=0.45Moderate, positive
  3. For a set of data, r=−0.3. What percent of the variation in y is explained by the linear relationship with x?9%
  4. Describe the direction and strength of a linear relationship with r=−0.55Moderate, negative
  5. Describe the direction and strength of a linear relationship with r=−0.1Weak, negative
  6. For a set of data, r=−0.1. What percent of the variation in y is explained by the linear relationship with x?1%
  7. For a set of data, r=−0.85. What percent of the variation in y is explained by the linear relationship with x?72.25%
  8. For a set of data, r=0.6. What percent of the variation in y is explained by the linear relationship with x?36%
  9. Describe the direction and strength of a linear relationship with r=0.7Strong, positive
  10. For a set of data, r=−0.4. What percent of the variation in y is explained by the linear relationship with x?16%
  11. For a set of data, r=0.95. What percent of the variation in y is explained by the linear relationship with x?90.25%
  12. For a set of data, r=−0.75. What percent of the variation in y is explained by the linear relationship with x?56.25%
  13. For a set of data, r=0.2. What percent of the variation in y is explained by the linear relationship with x?4%
  14. Describe the direction and strength of a linear relationship with r=−0.75Strong, negative
  15. Describe the direction and strength of a linear relationship with r=0.6Moderate, positive
  16. For a set of data, r=0.7. What percent of the variation in y is explained by the linear relationship with x?49%
  17. Describe the direction and strength of a linear relationship with r=−0.85Strong, negative
  18. For a set of data, r=0.45. What percent of the variation in y is explained by the linear relationship with x?20.25%
  19. Describe the direction and strength of a linear relationship with r=−0.4Moderate, negative
  20. Describe the direction and strength of a linear relationship with r=−0.3Weak, negative

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

r=0.8. What percent of the variation in y is explained?

  1. r² = 0.64.

The answer is 64%.

Where students go wrong

Reading a strong r as a steep line. r measures how tightly the points hug the line, not the slope: a nearly flat line can have r close to 1.

Also called correlation coefficient r, r squared or coefficient of determination.

Questions about these worksheets

Yes. Every correlation coefficient sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the correlation coefficient questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Reading a strong r as a steep line. r measures how tightly the points hug the line, not the slope: a nearly flat line can have r close to 1.