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
xy257356469574676xy2466070

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 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 =
3.Medium
xy2274406418471052xy510304050

The table gives 5 paired observations of x = advertising spend in k€ and y = sales in k€. Find Pearson's correlation coefficient r.

n = 5
r =
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 = 30Σy = 219Σx² = 220Σy² = 9769Σxy = 1398
r =
5.Hard
xy151352556765972xy5506070ŷ = 56

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 = 56?

n = 5ŷ = 56
x =
6.Hard
xy2641061382110231231xy510102030x = 11

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 (11, 22) is made. Find its residual e = y − ŷ.

n = 6(11, 22)
e =

Answer key

  1. 1. b = 5.6
  2. 2. b = 1.55
  3. 3. r = 0.9591
  4. 4. r = 0.9989
  5. 5. x = 3.836
  6. 6. e = −5.162

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