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 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 = 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
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The table gives 5 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 = 5Σx = 25Σy = 297Σx² = 135Σy² = 18053Σxy = 1547
r =
4.Medium
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The table gives 6 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 = 6
r² =
5.Hard
xy144253355469576xy24506070x = 4.5

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 (4.5, 73) is made. Find its residual e = y − ŷ.

n = 5(4.5, 73)
e =
6.Hard
xy16891910422117251412815231177xy15202530100150ŷ = 131

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. For which value x does the line predict ŷ = 131?

n = 6ŷ = 131
x =

Answer key

  1. 1. a = 28.8
  2. 2. a = 27
  3. 3. r = 0.9669
  4. 4. r² = 0.6801
  5. 5. e = 1.6
  6. 6. x = 23.67

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