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 intercept a.

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

n = 6
r =
4.Medium
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The table gives 5 paired observations of x = hours studied and y = exam score. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 5Σx = 20Σy = 334Σx² = 90Σy² = 22516Σxy = 1376
r =
5.Hard
xy21242162783610431253xy5102040x = 3

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 (3, 12) is made. Find its residual e = y − ŷ.

n = 6(3, 12)
e =
6.Hard
xy1559186221852487279830112xy152025306080100x = 16.5

The table gives 6 paired observations of x = temperature in °C and y = ice creams sold. Use the least-squares line ŷ = a + b·x. A new observation (16.5, 67) is made. Find its residual e = y − ŷ.

n = 6(16.5, 67)
e =

Answer key

  1. 1. b = 2.95
  2. 2. a = 48.53
  3. 3. r = 0.9981
  4. 4. r = 0.8839
  5. 5. e = −4
  6. 6. e = 4.595

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