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Linear Correlation

Gujarat Board · Class 12 · Statistics

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

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Key Topics to Revise

1

Core Concepts and Definitions

  • Correlation measures the simultaneous change in two variables due to a direct or indirect cause-effect relationship.
  • Linear correlation means the points of ordered pairs lie on or very near to a straight line — i.e., changes in two variables are nearly in constant proportion.
  • Positive Correlation: both variables move in the SAME direction (e.g., price and supply).
2

Scatter Diagram Method

  • Scatter Diagram is a graph where values of variable X are plotted on the X-axis and values of variable Y on the Y-axis.
  • Each ordered pair (xᵢ, yᵢ) is represented as a point on the graph.
  • The PATTERN of points tells us about the nature and approximate strength of correlation.
3

Karl Pearson's Product Moment Method

  • Karl Pearson's r is the most widely used and most efficient method for measuring linear correlation.
  • It uses all actual observations, not ranks.
  • Based on two assumptions: (1) Linear relationship between X and Y, (2) Cause-effect relationship exists between X and Y.
4

Properties of Correlation Coefficient – Detailed Study

  • Property 1 (Range): -1 ≤ r ≤ 1. This is the most fundamental property.
  • Property 2 (Unit-free): r has NO unit of measurement regardless of the units of X and Y.
  • Property 3 (Symmetry): r(X,Y) = r(Y,X). It does not matter which variable is X and which is Y.

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Full Notes

Key Concepts

Correlation is the simultaneous changeA scatter diagram is a graphicalKarl Pearson's method gives the exactUnderstanding these properties helps in solvingAfter calculating r

Frequently Asked Questions

What are the important topics in Linear Correlation for Gujarat Board Class 12 Statistics?
Linear Correlation 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 Correlation — 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.

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