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
xy1784209923114261282915332161xy202530100150

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. Find the intercept a.

n = 6
a =
2.Easy
xy22476981210161220xy5101020

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. Find the intercept a.

n = 6
a =
3.Medium
xy222328429528636xy246253035

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 =
4.Medium
xy17441956216623742584xy20256080

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 = 105Σy = 324Σx² = 2245Σy² = 21960Σxy = 7000
r =
5.Hard
xy133237342449557662xy246405060x = 4.5

The table gives 6 paired observations of x = advertising spend in k€ and y = sales in k€. Use the least-squares line ŷ = a + b·x. A new observation (4.5, 51) is made. Find its residual e = y − ŷ.

n = 6(4.5, 51)
e =
6.Hard
xy252363471578675785xy2466080x = 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 =

Answer key

  1. 1. a = −7.733
  2. 2. a = −1
  3. 3. r² = 0.7903
  4. 4. r = 0.9977
  5. 5. e = −1.724
  6. 6. ŷ = 76.61

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