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
xy264116178231028xy510102030

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 =
2.Easy
xy3635697859891110013116xy5106080100120

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 slope b.

n = 6
b =
3.Medium
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The table gives 6 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 = 6
r² =
4.Medium
xy24345366087010811281xy510406080

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 = 42Σy = 388Σx² = 364Σy² = 26280Σxy = 3000
r =
5.Hard
xy2641562182710341243xy5102040x = 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. Predict ŷ for x = 11.

n = 6x = 11
ŷ =
6.Hard
xy1567188321102241262714330146xy15202530100150x = 22.5

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 (22.5, 116) is made. Find its residual e = y − ŷ.

n = 6(22.5, 116)
e =

Answer key

  1. 1. a = 0.2
  2. 2. b = 5.171
  3. 3. r² = 0.9623
  4. 4. r = 0.9843
  5. 5. ŷ = 38.5
  6. 6. e = 4.833

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