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 = car age in years and y = price in k€. 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 = advertising spend in k€ and y = sales in k€. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 6Σx = 42Σy = 295Σx² = 364Σy² = 14977Σxy = 2238
r =
4.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 =
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 (4, 71) is made. Find its residual e = y − ŷ.

n = 5(4, 71)
e =
6.Hard
xy127227322421520619xy2462025ŷ = 26

The table gives 6 paired observations of x = car age in years and y = price in k€. Use the least-squares line ŷ = a + b·x. For which value x does the line predict ŷ = 26?

n = 6ŷ = 26
x =

Answer key

  1. 1. b = −0.7
  2. 2. a = 47.71
  3. 3. r = 0.9509
  4. 4. r² = 0.9357
  5. 5. e = −1.5
  6. 6. x = 1.618

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