Correlation and linear regression — Edexcel A-Level Statistics
Test yourself on Correlation and linear regression with PEARSON EDEXCEL A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Correlation and linear regression explained
This criterion requires you to carry out a hypothesis test for a correlation coefficient using critical values from tables.
Read the full explanation
First state the null hypothesis that the population correlation coefficient is zero and the alternative that it is not zero, or one-sided if the context requires. Choose a significance level, usually 0.05 unless told otherwise. Find the critical value from the appropriate table using the sample size n and the chosen significance level, taking care whether the test is one-tailed or two-tailed. Compare the absolute value of your calculated correlation coefficient with the critical value. If the absolute value exceeds the critical value, reject the null hypothesis and conclude there is significant evidence of a non-zero correlation in the population; otherwise do not reject it.
Your focus
- Formulate null and alternative hypotheses for a test of zero correlation.
- Read the correct critical value from tables using the sample size and significance level.
- Compare a calculated correlation coefficient with a critical value and interpret the result in context.
Correlation and linear regression exam tips
Marking Points
- States the null hypothesis that the population correlation coefficient is zero and the alternative hypothesis that it is not zero, or the appropriate one-sided alternative.
- Selects an appropriate significance level and identifies whether the test is one-tailed or two-tailed.
- Uses the correct table and reads the critical value using the sample size and significance level.
- Compares the absolute value of the calculated correlation coefficient with the critical value correctly.
- Draws a conclusion about the null hypothesis and states it in the context of the variables, including direction where appropriate.
Examiner Tips
- 💡Write out H₀ and H₁ clearly before calculating or comparing anything.
- 💡Quote the critical value you used and the calculated coefficient so the comparison is transparent.
- 💡Finish with a full-sentence conclusion that mentions the context and whether the evidence supports a non-zero correlation.
- 💡If the question gives a significance level, use it; if not, state that you are using 0.05 and proceed.
Common Mistakes
- Using the wrong degrees of freedom or sample size when reading the table; correction: check whether the table requires n or n − 2 and use the value stated in the table’s guidance.
- Forgetting to take the absolute value of a negative correlation coefficient before comparing with the critical value; correction: compare the magnitude with the critical value and keep the sign for the contextual conclusion.
- Confusing one-tailed and two-tailed critical values; correction: decide from the wording of the alternative hypothesis and use the matching column or row.
- Writing a conclusion that only says ‘reject H₀’ without context; correction: state what this means for the variables, for example that there is significant evidence of a positive association between them.