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 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 =
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 intercept a.

n = 6
a =
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 = load in kN and y = extension in mm. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 6Σx = 42Σy = 136Σx² = 364Σy² = 3782Σxy = 1170
r =
5.Hard
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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. A new observation (5, 6) is made. Find its residual e = y − ŷ.

n = 5(5, 6)
e =
6.Hard
xy352457556667764xy46556065ŷ = 58

The table gives 5 paired observations of x = hours studied and y = exam score. Use the least-squares line ŷ = a + b·x. For which value x does the line predict ŷ = 58?

n = 5ŷ = 58
x =

Answer key

  1. 1. b = 3.314
  2. 2. a = 36.36
  3. 3. r = 0.9887
  4. 4. r = 0.9853
  5. 5. e = −3.55
  6. 6. x = 4.647

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