11.
Explanation
The coefficient of correlation is a statistical measure used to quantify the strength and direction of the relationship between two variables in a dataset. It is a numerical value that indicates the degree to which two variables are associated or related. The coefficient of correlation is used to assess whether and how closely the values of two variables move together. It is a fundamental tool in statistics and data analysis, particularly in understanding the relationships between variables.
Range: The coefficient of correlation typically ranges from -1 to 1.
-1: A perfect negative correlation, meaning that as one variable increases, the other decreases in a perfectly linear manner.
0: No linear correlation; the two variables are independent of each other.
1: A perfect positive correlation, indicating that as one variable increases, the other also increases in a perfectly linear manner.
Strength: The magnitude of the correlation coefficient (the absolute value) indicates the strength of the relationship between the two variables. A coefficient closer to -1 or 1 suggests a stronger correlation, while a coefficient closer to 0 indicates a weaker or no linear correlation.
Direction: The sign of the correlation coefficient (positive or negative) indicates the direction of the correlation.
Positive Correlation: As one variable increases, the other tends to increase as well.
Negative Correlation: As one variable increases, the other tends to decrease.
Positive Correlation:
A positive correlation exists when two variables move in the same direction. In other words, as one variable increases, the other also tends to increase, and as one decreases, the other decreases. For example, there may be a positive correlation between the amount of time spent studying and test scores: the more time you spend studying, the higher your test scores are likely to be.
The coefficient of correlation for a positive correlation falls between 0 and 1. A value of 1 represents a perfect positive correlation.
Negative Correlation:
A negative correlation, on the other hand, occurs when two variables move in opposite directions. As one variable increases, the other tends to decrease, and vice versa. For example, there may be a negative correlation between the number of hours spent watching TV and the amount of exercise a person gets: the more TV someone watches, the less exercise they tend to get.
The coefficient of correlation for a negative correlation falls between -1 and 0. A value of -1 represents a perfect negative correlation