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
xy264156228301035xy510102030

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
xy3335457549681176xy510406080

The table gives 5 paired observations of x = advertising spend in k€ and y = sales in k€. Use the least-squares line ŷ = a + b·x. Find the intercept a.

n = 5
a =
3.Medium
xy264126188271034xy510102030

The table gives 5 paired observations of x = load in kN and y = extension in mm. Their sums are given. Find Pearson's correlation coefficient r from these sums.

n = 5Σx = 30Σy = 97Σx² = 220Σy² = 2389Σxy = 724
r =
4.Medium
xy143350560774983xy5406080

The table gives 5 paired observations of x = advertising spend in k€ and y = sales in k€. Find the coefficient of determination r² of the least-squares line.

n = 5
r² =
5.Hard
xy181082111624136271593017533186xy202530150x = 31.5

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 (31.5, 185) is made. Find its residual e = y − ŷ.

n = 6(31.5, 185)
e =
6.Hard
xy12421731741251268xy24610152025x = 4.5

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. Predict ŷ for x = 4.5.

n = 6x = 4.5
ŷ =

Answer key

  1. 1. a = −0.3
  2. 2. a = 17.05
  3. 3. r = 0.9969
  4. 4. r² = 0.9887
  5. 5. e = 4.619
  6. 6. ŷ = 12.14

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