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 = hours studied and y = exam score. 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 = load in kN and y = extension in mm. 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 = hours studied and y = exam score. Find the coefficient of determination r² of the least-squares line.

n = 5
r² =
4.Medium
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The table gives 5 paired observations of x = advertising spend in k€ and y = sales in k€. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 5Σx = 15Σy = 151Σx² = 55Σy² = 4597Σxy = 471
r =
5.Hard
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The table gives 5 paired observations of x = hours studied and y = exam score. Use the least-squares line ŷ = a + b·x. Predict ŷ for x = 2.5.

n = 5x = 2.5
ŷ =
6.Hard
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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. A new observation (4, 52) is made. Find its residual e = y − ŷ.

n = 6(4, 52)
e =

Answer key

  1. 1. b = 3.7
  2. 2. b = 3.057
  3. 3. r² = 0.9528
  4. 4. r = 0.9383
  5. 5. ŷ = 48.45
  6. 6. e = −3.586

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