13.
Explanation
Regression is a statistical concept and technique used to understand and quantify the relationship between two or more variables in a dataset. Specifically, it is used to analyse the relationship between a dependent variable (also known as the response variable) and one or more independent variables (predictors or explanatory variables).
In a bivariate series, there are typically two variables involved: one dependent variable (Y) and one independent variable (X). Regression analysis in this context helps us determine how changes in the independent variable (X) affect the dependent variable (Y). The result of a bivariate regression analysis is often represented as a linear equation of the form:
Y=a+bX
Here's why there are two regression lines in a bivariate series and whether there can be just one regression line:
Two Regression Lines: In a bivariate series, there are typically two regression lines because you are examining the relationship between two variables, Y and X. The first regression line represents how the independent variable X predicts or explains the variation in the dependent variable Y. This line is often referred to as the "regression line of Y on X" and is used to make predictions or estimate the
Y=a+bX, where "a" is the intercept and "b" is the slope of the line.
Two Perspectives: The second regression line represents how the independent variable Y predicts the variation in the dependent variable X. This line is referred to as the "regression line of X on Y" and is used to make predictions or estimate the value of X for a given value of Y. The equation for this line is
X=c+dY, with "c" as the intercept and "d" as the slope of the line.
One Regression Line: In some cases, the two regression lines may be very similar, and if the relationship between the two variables is perfectly linear (meaning there's no measurement error or variability), you may obtain the same regression line regardless of whether you treat Y as the dependent or independent variable. However, in real-world situations, it's common for the relationship to be asymmetric, and the two regression lines can differ.