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When a functional relationship exists, determining the value of x necessarily determines the value of y. However, although the value of x is determined, the value of y is not precisely determined, therefore, it may not be possible to say that the two are unrelated.
A typical example of this phenomenon is the relationship between height and weight. This correlation can be explained as follows:
Correlation
The following table shows the height and weight measurements of 10 students.
[Table] Subjects’ height and weight
Draw a point graph with height on the y-axis (vertical axis) and weight on the x-axis (horizontal axis). This diagram is called a “correlation diagram” or a “scatter diagram.”
[Figure] Correlation diagram between height and weight (scatter diagram)
Looking at the correlation diagram, there is no clear relationship that states, “If your weight is determined, your height will be determined.” Therefore, the relationship between weight and height cannot be expressed using relational expressions. However, there is a trend that the heavier the person, the greater their height; therefore, it cannot be said that weight and height are completely unrelated.
This property of two items changing simultaneously with a considerable degree of regularity is called “correlation.” Furthermore, when a relationship exists between two items, x and y, it is said that there is a correlation between x and y.
Examining the causal relationships between variables using correlations is called “correlation analysis.”
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