Correlation
About correlation
Purpose – To measure the relationship between two variables. Students will normally learn the formula in calculating correlation in A-level mathematics class. However, the basic concept on the correlation which is the scatter plot maybe be introduce during the O-level mathematics lessons.
Formula
Correlation = Covariance of the two variables, x & y and divide it by the standard deviation of x and standard deviation of y.
How to determine the siginificance of the correlation value
Taking the sample size, n, then minus it with 2 in order to obtain the degree of freedom in order to obtain the critical value from the statistics table. df = n – 2.
Question
Calcuate the correlation values for the following set of the variables.
1. The correlation between Variable 1 & Variable 2.
| variable 1 | variable 2 |
| 1 | 4 |
| 1 | 4 |
| 4 | 2 |
| 3 | 4 |
| 5 | 1 |
| 4 | 2 |
| 1 | 2 |
| 0 | 0 |
| 1 | 1 |
| 5 | 3 |
| 4 | 2 |
| 4 | 4 |
| 5 | 5 |
| 0 | 4 |
2. The correlation between Variable 3 & Variable 4.
| variable 3 | variable 4 |
| 4 | 4 |
| 5 | 2 |
| 1 | 1 |
| 1 | 2 |
| 5 | 0 |
| 0 | 0 |
| 5 | 2 |
| 1 | 3 |
| 5 | 0 |
| 1 | 2 |
| 5 | 4 |
| 5 | 3 |
| 3 | 4 |
| 2 | 2 |
3. The correlation between Variable 5 & Variable 6.
| variable 5 | variable 6 |
| 1 | 1 |
| 5 | 5 |
| 3 | 3 |
| 3 | 4 |
| 2 | 3 |
| 5 | 1 |
| 3 | 2 |
| 2 | 1 |
| 2 | 5 |
| 5 | 3 |
| 4 | 4 |
| 4 | 4 |
| 4 | 5 |
| 4 | 5 |
4. The correlation between Variable 7 & Variable 8.
| variable 7 | variable 8 |
| 5 | 2 |
| 5 | 4 |
| 3 | 0 |
| 1 | 5 |
| 0 | 2 |
| 3 | 5 |
| 2 | 3 |
| 5 | 2 |
| 2 | 5 |
| 1 | 2 |
| 5 | 1 |
| 2 | 5 |
| 0 | 5 |
| 2 | 1 |
5. The correlation between variable 9 & variable 10.
| variable 9 | variable 10 |
| 5 | 1 |
| 1 | 5 |
| 1 | 1 |
| 4 | 4 |
| 3 | 4 |
| 0 | 0 |
| 3 | 2 |
| 4 | 2 |
| 5 | 1 |
| 0 | 2 |
| 3 | 4 |
| 4 | 3 |
| 2 | 3 |
| 4 | 5 |
Answer
- Correlation between variable 1 & variable 2 = 0.129
- Correlation between variable 3 & variable 4 = 0.16
- Correlation between variable 5 & variable 6 = 0.335
- Correlation between variable 7 & variable 8 = -0.304
- Correlation between variable 9 & variable 10 = 0.138
About the Math Tutor - Dr Loo
I am a PhD holder with 9 years of teaching experience at secondary school and university. My expertizes are mathematics, statistics, econometrics, finance and machine learning.
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