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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

  1. Correlation between variable 1 & variable 2 = 0.129
  2. Correlation between variable 3 & variable 4 = 0.16
  3. Correlation between variable 5 & variable 6 = 0.335
  4. Correlation between variable 7 & variable 8 = -0.304
  5. Correlation between variable 9 & variable 10 = 0.138

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