Home Class 11 Applied Maths Chapter 12: Regression Analysis
CBSE Applied Maths (2026-27) Unit V: Descriptive Statistics Weightage: ~10 Marks in Unit

Chapter 12: Regression Analysis

Learn predictive modeling, lines of regression, least squares method, regression coefficients, and intersection points.

3 Exercises
CBSE Curriculum Aligned
Interactive Quizzes & Solutions

Chapter Exercises & Topics

Select any exercise to access theory notes, formulas, practice drills, and mini tests.

Exercise 12.1 45 mins

Concept and Foundations of Regression

  • Meaning, distinction between correlation and regression
  • Dependent vs. independent variables
  • Importance in business forecasting, machine learning, and artificial intelligence
Study Exercise Mini Test
Exercise 12.2 45 mins

Lines of Regression

  • Regression line of Y on X: (Y - Ȳ) = b_yx(X - X̄)
  • Regression line of X on Y: (X - X̄) = b_xy(Y - Ȳ)
  • Derivation using the Method of Least Squares
Study Exercise Mini Test
Exercise 12.3 45 mins

Regression Coefficients

  • Regression coefficients b_yx = r(σ_y/σ_x) and b_xy = r(σ_x/σ_y)
  • Geometric mean property: r = ±√(b_yx · b_xy)
  • Same algebraic sign property (r, b_yx, b_xy share identical signs)
  • Arithmetic mean property: (b_yx + b_xy) / 2 >= r
  • Invariance under change of origin, but variance under change of scale
Study Exercise Mini Test

Chapter 12 Core Formula Sheet

Quick-glance formula revision for examination and numerical problem-solving:

  • $$\text{Correlation measures association; Regression predicts values.}$$
  • $$\text{Dependent variable (Y) predicted from independent variable (X).}$$
  • $$Y - \bar{Y} = b_{yx}(X - \bar{X})$$
  • $$X - \bar{X} = b_{xy}(Y - \bar{Y})$$
  • $$\text{Both lines pass through } (\bar{X}, \bar{Y})$$
  • $$b_{yx} = r \frac{\sigma_y}{\sigma_x}, \quad b_{xy} = r \frac{\sigma_x}{\sigma_y}$$
  • $$r = \pm\sqrt{b_{yx} \cdot b_{xy}}, \quad \frac{b_{yx} + b_{xy}}{2} \ge r$$
Ch 11: Correlation Analysis All Chapters Syllabus Ch 13: Interests and Annuities