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Pearson’s correlation coefficient, also known as Pearson’s r, is a statistical measurement that defines the strength of relationship between two variables and their association with each other.Â
In simple words, Pearson correlation coefficient determines any change in one variable that is influenced by the other related variable. Pearson correlation coefficient is influenced by the concept of covariance which makes it a best method to determine the relationship and interdependency between the two variables.Â
Example: a kid’s age increases with time. As time grows, its age starts increasing in years too.Â
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Pearson correlation coefficient looks at the relationship between two variables and determine the influence of one on the other. It draws a line through the data of both of those relationships and this relationship between two variables is defined through a Pearson correlation coefficient calculator.Â
Generally there are two types of relationships between two variables:
Positive linear relationship – when one variable goes up, the other goes up too. Example: as the number of day increases, the plant grows (increase) too.Â
Negative linear relationship – when one variable goes up the other one goes down. Example: when a car is travelling to a destination, as its distance travelled increases, the distance till the destination decreases.Â
Being a statistical measurement, it is obvious that there is going to be a systematic way of calculating the relationship between two variables. In this section we will see what the Pearson correlation coefficient formula is and what it means:
Where the variables mean:
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In this section, we will be taking an example: the height of children increases with their age (not considering some exceptions)
Child | Age (yrs)Â x | Height(ft) y | xy | x2 | y2 |
1 | 1 | 2 | Â | Â | Â |
2 | 4 | 3 | Â | Â | Â |
3 | 10 | 4 | Â | Â | Â |
4 | 13 | 5 | Â | Â | Â |
5 | 20 | 6 | Â | Â | Â |
Â
Â
Child | Age (yrs)Â x | Height(ft) y | xy | x2 | y2 |
1 | 1 | 2 | 2 | 1 | 4 |
2 | 4 | 3 | 12 | 8 | 9 |
3 | 10 | 4 | 40 | 100 | 16 |
4 | 13 | 5 | 65 | 169 | 25 |
5 | 20 | 6 | 120 | 400 | 36 |
Child | Age (yrs)Â x | Height(ft) y | xy | x2 | y2 |
1 | 1 | 2 | 2 | 1 | 4 |
2 | 4 | 3 | 12 | 8 | 9 |
3 | 10 | 4 | 40 | 100 | 16 |
4 | 13 | 5 | 65 | 169 | 25 |
5 | 20 | 6 | 120 | 400 | 36 |
Total | 48 | 20 | 239 | 678 | 90 |
Â
Hence, according to the formula, the substitutions will look like:
5(239) – (48) (20) / √ [5(678) – (48)2] [5(90) – (20)2]
1195 – 960 / √ (3390 – 2304) (450 – 400)
235 / √ (1086)(50)
235 / √54300
235 / 233.02
1.00
In our example, as our Pearson correlation coefficient value is 1, the strength of association between the two variables age and height is large.Â
The Pearson correlation coefficient value you get highly depend on the sample size you choose and what measure you take. A graphical representation of the relationship will tell you how the variables are related even before you start your measurement. The scatterplots do the work. If they are close to the line, then the relationship is strong, else if they are scattered away from the line, the relationship is weak. If the line is almost parallel to the x-axis with the scatterplots randomly plotted on the graph, we can say that there is no correlation between the variables.Â
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As discussed how the scatterplot represents how strong or weak the relationship is, we will be seeing how it actually looks like:
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