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 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 6 paired observations of x = advertising spend in k€ and y = sales in k€. Find Pearson's correlation coefficient r.

n = 6
r =
4.Medium
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The table gives 6 paired observations of x = temperature in °C and y = ice creams sold. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 6Σx = 147Σy = 616Σx² = 3759Σy² = 67678Σxy = 15911
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. A new observation (8, 73) is made. Find its residual e = y − ŷ.

n = 5(8, 73)
e =
6.Hard
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The table gives 6 paired observations of x = advertising spend in k€ and y = sales in k€. Use the least-squares line ŷ = a + b·x. Predict ŷ for x = 3.5.

n = 6x = 3.5
ŷ =

Answer key

  1. 1. a = 3.7
  2. 2. b = 5.186
  3. 3. r = 0.975
  4. 4. r = 0.9799
  5. 5. e = 3.1
  6. 6. ŷ = 49.62

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