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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xy3425487549641174xy51040506070

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 =
2.Easy
xy3675797909971111713122xy51080100120

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
xy23496178211027xy5101020

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 = 77Σx² = 220Σy² = 1549Σxy = 582
r =
4.Medium
xy165718702082228524104xy206080100

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 = 100Σy = 398Σx² = 2040Σy² = 32914Σxy = 8178
r =
5.Hard
xy263364466579685792xy246708090x = 5.5

The table gives 6 paired observations of x = hours studied and y = exam score. Use the least-squares line ŷ = a + b·x. Predict ŷ for x = 5.5.

n = 6x = 5.5
ŷ =
6.Hard
xy346450553653764xy465060x = 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, 49) is made. Find its residual e = y − ŷ.

n = 5(4.5, 49)
e =

Answer key

  1. 1. a = 28.4
  2. 2. b = 5.657
  3. 3. r = 0.9956
  4. 4. r = 0.9815
  5. 5. ŷ = 81.15
  6. 6. e = −2.25

Full step-by-step solutions: practise this topic on examproblems.com.