The Lines of Regression Intersect at the Point
By BYJU'S Exam Prep
Updated on: November 9th, 2023
The point of intersection of Regression lines is at (x‾, y‾). Regression is a handy and essential tool in statistical analysis. It explains the nature of the relationship between two variables. In addition, regression analysis can predict the value of a dependent variable based on an independent variable.
Table of content
Lines of Regression
The line perfectly matches the data, ensuring that the total distance between the line and the graph’s points is as little as possible. In other terms, the phrase “regression line” refers to a line that is utilized to reduce the squared forecasting deviations.
Regression is a statistical approach used in the fields of finance, investing, and other disciplines that aim to ascertain the nature and strength of the connection between one dependent variable and several independent variables.
When predicting, regression lines are useful. Its objective is to explain how the dependent variable (in this case, “y”) and one or more independent variables (in this case, “x”) are related. By entering different values for the independent variables, an analyst may predict the future behaviors of the dependent variables using the equation obtained from the regression line.
Lines of Regression Intersection Point
Let’s describe the two lines first to know the significance of the point of intersection of the two regression lines.
- The line of regression of y on x is given by: y-ȳ=byx (x-x‾)
- The sequence of regression of x on y is provided by: x-x‾=bxy (y-ȳ)
- The correlation coefficient r2=byx*bxy, where by and by are regression coefficients.
- The point of intersection of two lines is at (x‾, y‾)
Summary:
The Lines of Regression Intersect at the Point?
The end of the intersection of regression lines is (x‾, y‾), that is, the mean. The point of intersection of regression lines gives the mean. This is because the two lines coincide and pass-through this common point. Therefore, this is the solution for both equations.
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