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
xy353463564668777886xy4686080

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 =
2.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 =
3.Medium
xy123223316413511xy241520

The table gives 5 paired observations of x = car age in years and y = price in k€. Find the coefficient of determination r² of the least-squares line.

n = 5
r² =
4.Medium
xy16431956226025742889xy2025406080

The table gives 5 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 = 5Σx = 110Σy = 322Σx² = 2510Σy² = 21982Σxy = 7414
r =
5.Hard
xy25486158181027xy5101020x = 3

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. A new observation (3, 1) is made. Find its residual e = y − ŷ.

n = 5(3, 1)
e =
6.Hard
xy2641061381610161219xy5105101520ŷ = 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. For which value x does the line predict ŷ = 11?

n = 6ŷ = 11
x =

Answer key

  1. 1. a = 35.34
  2. 2. b = −2.7
  3. 3. r² = 0.9263
  4. 4. r = 0.9858
  5. 5. e = −5.5
  6. 6. x = 5.101

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