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Correlation and Regression Practice Problems with Solutions - IB Year 12

IB Year 12 | Math | Correlation and Regression
Name: _________________________ Date: _________________________ Score: _______ / 40

Correlation measures the strength and direction of a linear relationship between two variables, and r always lands between −1 and 1, so this IB sheet deals with how tightly data follows a straight line. The key also names a strong positive and a strong negative correlation.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. Correlation measures the
(a) strength and direction of a linear relationship between two variables(b) cause of one variable(c) difference between two variables(d) average of two variables
2. The correlation coefficient r takes values between
(a) −1 and 1(b) 0 and 1(c) −1 and 0(d) 0 and 100
3. If r = 0.9, the correlation is
(a) strong positive(b) strong negative(c) weak positive(d) zero
4. If r = −0.8, the correlation is
(a) strong negative(b) strong positive(c) zero(d) perfect positive
5. A correlation coefficient of exactly 1 means
(a) perfect positive linear correlation(b) no correlation(c) perfect negative correlation(d) weak correlation
6. A regression line is used to
(a) predict a value of y from a value of x(b) prove causation(c) find the mean(d) find the median

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. What does the correlation coefficient measure?
8. State the range of the correlation coefficient r.
9. What does r = 0 indicate?
10. Distinguish between correlation and causation.
11. Write the equation of a regression line.
12. What is a scatter diagram used for?
13. What does a perfect negative correlation look like on a scatter diagram?
14. Give one example of two variables that might be positively correlated.

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. Given the regression line y = 2x + 5, find the predicted value of y when x = 3.
16. Given the regression line y = −3x + 10, find the predicted value of y when x = 2.
17. A set of data gives r = 0.98. Describe the correlation in words.
18. Given the regression line y = 4x + 2, find the predicted value of y when x = 5.
19. Two variables have a correlation coefficient of r = −0.95. Describe the relationship.
20. Given the regression line y = 1.5x − 3, find the predicted value of y when x = 4.

Answer Key

1. a) strength and direction of a linear relationship between two variables
2. a) −1 and 1
3. a) strong positive
4. a) strong negative
5. a) perfect positive linear correlation
6. a) predict a value of y from a value of x
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End of Worksheet

People Also Ask

What does correlation measure?

The strength and direction of a linear relationship between two variables, option (a) in this worksheet (Q1).

What values can r take?

Between −1 and 1, option (a) in this worksheet (Q2).

What does a value near −1 indicate?

A strong negative correlation, from the answer key on this page.

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Also see a full correlation and regression solution worked out.