Which of the following has a range from -1 to +1? Correlation Heritability Regression Standard Deviation
The correct answer and explanation is:
The correct answer is Correlation.
Explanation:
Correlation is a statistical measure that expresses the extent to which two variables are linearly related. Its values range between -1 and +1:
- A correlation of +1 means a perfect positive linear relationship between the two variables: as one increases, the other increases proportionally.
- A correlation of -1 means a perfect negative linear relationship: as one variable increases, the other decreases proportionally.
- A correlation of 0 means no linear relationship between the variables.
Because correlation coefficients are standardized measures, they are always confined within the limits of -1 and +1. This bounded range helps in interpreting the strength and direction of the linear relationship between variables.
Why not the others?
- Heritability: This measures the proportion of total phenotypic variance in a trait that is attributable to genetic variance within a population. Heritability values range from 0 to 1, not negative. A heritability of 0 means no genetic contribution, and 1 means the trait is fully determined by genetics (in that population and environment).
- Regression: Regression refers to modeling the relationship between a dependent variable and one or more independent variables. The regression coefficients (slopes) can take any real number value—there is no fixed range like -1 to +1.
- Standard Deviation: This is a measure of variability or spread in data. Since it represents the average distance of data points from the mean, it is always non-negative (≥ 0) and can take any positive value, depending on data variability. It never goes negative, and it definitely doesn’t have an upper bound of +1.
Summary
- Correlation coefficients are constrained between -1 and +1.
- Heritability ranges between 0 and 1.
- Regression coefficients and standard deviations can take a wide range of values, with no fixed limits like correlation.
This bounded range of correlation makes it a very useful standardized metric to understand the strength and direction of linear relationships across different fields including statistics, biology, social sciences, and more.