Biostatistics: Regression | Zoology Optional Notes for UPSC PDF Download

Introduction to Regression

• Regression analysis is a statistical technique used for estimating and predicting the average value of one variable based on a specified value of another variable.
• The process involves deriving a suitable equation from available bivariate data, known as the Regression equation, and visualizing it as the Regression curve.

• The Regression equation requires the determination of the Regression coefficient (b), which signifies the strength and direction of the relationship between the variables.
• The Regression coefficient (b) is calculated through two different methods, depending on whether it's for y on x or x on y. These methods consider the standard deviations of y (δy) and x (δx).

Regression Line

• When plotting bivariate data on a graph, the distribution of data points often exhibits a discernible pattern, indicating a relationship.
• In cases where the relationship appears linear, the least square method can be employed to derive the Regression line.
• The linear relationship between two variables can be expressed as y = bx + a, where 'b' represents the slope of the line, and 'a' denotes the intercept.
• Utilizing the values in the Regression equation, we can easily obtain the equation of the Regression line. An illustrative example (Example 1) further elucidates this process.

• The Regression equation of x on y is determined as.
  
• The Regression equation of y on x is computed as [Insert Equation].
  

Significance of Regression

• Regression analysis plays a vital role in estimating or predicting one variable when the other is known.
• It also facilitates extrapolation, allowing us to predict values of one variable when the other is assumed, expanding its practical utility.

Difference Table for Regression Coefficients Calculation: