PERPENDICULAR REGRESSION Meaning and
Definition
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Perpendicular regression is a statistical technique used to analyze the relationship between two variables. It is a method to determine the best-fitting line that describes the association between the variables in a dataset. Unlike traditional linear regression, where the line of best fit is determined by minimizing the vertical distance between the data points and the line, perpendicular regression minimizes the perpendicular distances between the data points and the line.
The procedure starts by selecting an initial line and then calculates the perpendicular distances between the data points and the line. These distances are then squared to ensure positive values. The regression line is optimized by minimizing the sum of these squared perpendicular distances. This is done iteratively until the line that produces the minimum sum of squared perpendicular distances is found.
Perpendicular regression is particularly useful when the relationship between variables is nonlinear or when there is potential heteroscedasticity (unequal variance) in the data. It is commonly used in fields such as physics, geology, and engineering, where relationships between variables may not be strictly linear.
The output of a perpendicular regression analysis includes the equation of the regression line, which can be used to predict values of one variable based on the other. Additionally, an assessment of the goodness-of-fit, such as the coefficient of determination (R-squared), can be obtained to evaluate the strength of the relationship between the variables.
Etymology of PERPENDICULAR REGRESSION
The word "perpendicular regression" does not have a specific etymology as it is a combination of two individual terms: "perpendicular" and "regression".
1. "Perpendicular" comes from the Latin word "perpendiculum", meaning "plumb line" or "vertical". It is derived from the combination of "per-" (meaning "through") and "pendere" (meaning "to hang").
2. "Regression" has its roots in the Latin word "regressus", which means "a retreat" or "a going back". It is derived from the combination of "re-" (meaning "back") and "gradi" (meaning "to step").
When combined, "perpendicular regression" refers to a statistical method used to find the best-fitting line or curve that minimizes the perpendicular distance between data points and the line or curve.
