Negative relationship
(Redirected from Inverse relationship)
Negative Relationship[edit | edit source]
A negative relationship is a type of correlation between two variables where an increase in one variable is associated with a decrease in the other. This concept is fundamental in statistics and is often visualized using a scatter plot where the data points tend to slope downwards from left to right.
Characteristics[edit | edit source]
In a negative relationship, as one variable increases, the other variable tends to decrease. This inverse relationship can be quantified using the Pearson correlation coefficient, which ranges from -1 to 1. A coefficient of -1 indicates a perfect negative linear relationship, while a coefficient of 0 indicates no linear relationship.
Negative relationships are often observed in various fields such as economics, psychology, and biology. For example, in economics, there might be a negative relationship between the price of a product and the quantity demanded, known as the law of demand.
Examples[edit | edit source]
- Economics: The law of demand states that, all else being equal, as the price of a good increases, the quantity demanded decreases, illustrating a negative relationship.
- Biology: In ecology, there can be a negative relationship between the population size of predators and prey. As the number of predators increases, the number of prey tends to decrease.
- Psychology: In studies of stress and performance, there is often a negative relationship where increased stress levels can lead to decreased performance on tasks.
Mathematical Representation[edit | edit source]
Mathematically, a negative relationship can be represented by a linear equation of the form:
- \( y = mx + c \)
where \( m \) is the slope of the line. In a negative relationship, \( m \) is negative, indicating that as \( x \) increases, \( y \) decreases.
Visualizing Negative Relationships[edit | edit source]
Negative relationships are often visualized using scatter plots. In these plots, data points are plotted on a two-dimensional graph, and a line of best fit is drawn to represent the relationship. The slope of this line indicates the direction and strength of the relationship.
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