Unit Standard number 9015
Apply Knowledge of statistics and probability to critically interrogate and effectively
communicate findings on life related problems
1. Below is a sample of years of education and income for five individuals. (Page 35)
Education Income
12 33
15 41
8 18
10 28
17 53
1. What is the independent variable and what is the dependent variable?
2. Calculate the Correlation Coefficient.
3. What does this indicate?
The independent variable is Education and the dependent variable is the Income.
Person Education =x Income=y xy x^2 y^2
1 12 33 396 144 1089
2 15 41 615 225 1681
3 8 18 144 64 324
4 10 28 280 100 784
5 17 53 901 289 2809
Total 62 173 2336 822 6687
N = number of pairs of scores 5
∑ xy sum of the products of paired scores 2336
∑x =sum of x scores 62
∑y =sum of y scores 173
∑ x^2 =sum of squared x scores 822
∑ y^2 =sum of squared y scores 6687
𝑛 𝑥𝑦 − 𝑥 𝑦
𝑟=
𝑛 𝑥2 − 𝑥 2 × 𝑛 𝑦2 − 𝑦 2
5 × 2336 − 62 × 173
𝑟=
(5 × 822 − 622 ) × (5 × 6687 − 1732 )
∴ r = 0.987874
- The number is positive, which implies that there is a positive linear relationship. i.e. an
increase in years of education corresponds to an increase in Income.
Note: Causality cannot be assumed, inasmuch as there is a linear relationship.
- The figure is very close to +1, which implies that there’s a strong positive linear
relationship.
1
Apply Knowledge of statistics and probability to critically interrogate and effectively
communicate findings on life related problems
1. Below is a sample of years of education and income for five individuals. (Page 35)
Education Income
12 33
15 41
8 18
10 28
17 53
1. What is the independent variable and what is the dependent variable?
2. Calculate the Correlation Coefficient.
3. What does this indicate?
The independent variable is Education and the dependent variable is the Income.
Person Education =x Income=y xy x^2 y^2
1 12 33 396 144 1089
2 15 41 615 225 1681
3 8 18 144 64 324
4 10 28 280 100 784
5 17 53 901 289 2809
Total 62 173 2336 822 6687
N = number of pairs of scores 5
∑ xy sum of the products of paired scores 2336
∑x =sum of x scores 62
∑y =sum of y scores 173
∑ x^2 =sum of squared x scores 822
∑ y^2 =sum of squared y scores 6687
𝑛 𝑥𝑦 − 𝑥 𝑦
𝑟=
𝑛 𝑥2 − 𝑥 2 × 𝑛 𝑦2 − 𝑦 2
5 × 2336 − 62 × 173
𝑟=
(5 × 822 − 622 ) × (5 × 6687 − 1732 )
∴ r = 0.987874
- The number is positive, which implies that there is a positive linear relationship. i.e. an
increase in years of education corresponds to an increase in Income.
Note: Causality cannot be assumed, inasmuch as there is a linear relationship.
- The figure is very close to +1, which implies that there’s a strong positive linear
relationship.
1
