Linear regression & correlation worksheet with answers

Free printable Linear regression & correlation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
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The table gives 5 paired observations of x = load in kN and y = extension in mm. Use the least-squares line ŷ = a + b·x. Find the slope b.

n = 5
b =
2.Easy
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The table gives 6 paired observations of x = hours studied and y = exam score. Use the least-squares line ŷ = a + b·x. Find the slope b.

n = 6
b =
3.Medium
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The table gives 5 paired observations of x = load in kN and y = extension in mm. Find Pearson's correlation coefficient r.

n = 5
r =
4.Medium
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The table gives 6 paired observations of x = car age in years and y = price in k€. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 6Σx = 21Σy = 119Σx² = 91Σy² = 2489Σxy = 372
r =
5.Hard
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The table gives 6 paired observations of x = load in kN and y = extension in mm. Use the least-squares line ŷ = a + b·x. A new observation (5, 12) is made. Find its residual e = y − ŷ.

n = 6(5, 12)
e =
6.Hard
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The table gives 5 paired observations of x = car age in years and y = price in k€. Use the least-squares line ŷ = a + b·x. Predict ŷ for x = 4.5.

n = 5x = 4.5
ŷ =

Answer key

  1. 1. b = 1.7
  2. 2. b = 3.143
  3. 3. r = 0.9375
  4. 4. r = −0.9372
  5. 5. e = −4.995
  6. 6. ŷ = 15.05

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