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 intercept a.

n = 5
a =
2.Easy
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The table gives 5 paired observations of x = advertising spend in k€ and y = sales in k€. Use the least-squares line ŷ = a + b·x. Find the intercept a.

n = 5
a =
3.Medium
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The table gives 6 paired observations of x = advertising spend in k€ and y = sales in k€. Find the coefficient of determination r² of the least-squares line.

n = 6
r² =
4.Medium
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The table gives 6 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 = 6Σx = 27Σy = 368Σx² = 139Σy² = 23136Σxy = 1752
r =
5.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 (10, 92) is made. Find its residual e = y − ŷ.

n = 6(10, 92)
e =
6.Hard
xy143243349457560665xy2465060ŷ = 58

The table gives 6 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 = 6ŷ = 58
x =

Answer key

  1. 1. a = 2.7
  2. 2. a = 35.2
  3. 3. r² = 0.9692
  4. 4. r = 0.9652
  5. 5. e = 3.5
  6. 6. x = 4.57

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