Skip to main content
Super TutorResources
Chapter 5 of 9
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Linear Regression

Gujarat Board · Class 12 · Statistics

Quick revision notes for Linear Regression — Gujarat Board Class 12 Statistics. Key concepts, formulas, and definitions for last-minute revision.

5 concepts

Interactive on Super Tutor

Studying Linear Regression? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

Key Topics to Revise

1

1. Core Concepts: Regression vs. Correlation

  • Correlation measures the strength and direction of association between two variables but cannot predict values.
  • Regression establishes a mathematical (functional) relationship that enables prediction of one variable from another.
  • The term 'regression' was coined by Sir Francis Galton from his study of heights of 1000 father-son pairs — sons' heights 'regressed' (returned) toward the mean.
2

2. Fitting the Regression Line – Method of Least Squares

  • Two methods exist: (1) Method of Scatter Diagram — quick but subjective; (2) Method of Least Squares — objective and gives the best-fit line.
  • The scatter diagram method is subjective because different people draw different lines, giving different estimates for the same X value.
  • The Method of Least Squares finds the line Ŷ = a + bX that minimises the sum of squared vertical errors: Σ(Yi − Ŷi)² = minimum.
3

3. Step-by-Step Worked Examples

  • EXAMPLE 1 (Basic – from raw data): Find the regression line of Y on X for the data: X: 1, 2, 3, 4, 5 and Y: 3, 5, 4, 6, 7
  • Step 1: Set up the calculation table.
  • Step 2: Compute all required sums: n, ΣX, ΣY, ΣX², ΣXY.
4

4. Regression Coefficient – Properties and Interpretation

  • The regression coefficient b represents the estimated change in Y for a one-unit increase in X.
  • If b > 0: Y increases as X increases (positive relationship). If b < 0: Y decreases as X increases (negative relationship).
  • Sign of b is always the same as the sign of correlation coefficient r (since σX and σY are always positive).

Get complete notes with diagrams and examples

Full Notes

Key Concepts

Regression means 'to return toIn any causeThe linear regression modelStepsThe best

Frequently Asked Questions

What are the important topics in Linear Regression for Gujarat Board Class 12 Statistics?
Linear Regression covers several key topics that are frequently asked in Gujarat Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Linear Regression — Gujarat Board Class 12 Statistics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Linear Regression

All 9 chapters — Gujarat Board Class 12 Statistics Revision Notes

For serious students

Get the full Linear Regression chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Gujarat Board Class 12 Statistics.

Try Super Tutor Free
Try the full chapter — Free