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 = hours studied and y = exam score. 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 = load in kN and y = extension in mm. 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 5 paired observations of x = hours studied and y = exam score. Find the coefficient of determination r² of the least-squares line.

n = 5
r² =
4.Medium
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The table gives 6 paired observations of x = hours studied and y = exam score. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 6Σx = 27Σy = 314Σx² = 139Σy² = 16762Σxy = 1479
r =
5.Hard
xy1353515577739861192xy510406080ŷ = 67

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. For which value x does the line predict ŷ = 67?

n = 6ŷ = 67
x =
6.Hard
xy164118422047226624662677xy2025406080x = 23

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 (23, 67) is made. Find its residual e = y − ŷ.

n = 6(23, 67)
e =

Answer key

  1. 1. a = 46.4
  2. 2. a = −0.5
  3. 3. r² = 0.9402
  4. 4. r = 0.8694
  5. 5. x = 6.23
  6. 6. e = 2.757

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