Chapter 3 of 9
Syllabus
Linear Correlation — Syllabus
Gujarat Board · Class 12 · Statistics
What Linear Correlation covers in Gujarat Board Class 12 Statistics: 4 topics, for the 2026-27 session. Topics include Core Concepts and Definitions.
9 formulas & key relations5 concepts
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4 Topics · Gujarat Board Class 12 Statistics · 2026-27
Topics in Linear Correlation
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.
Key Concepts
Central concept: Linear Correlation
Definition of CorrelationTypes of CorrelationMethods of Studying CorrelationScatter Diagram MethodKarl Pearson MethodSpearman Rank CorrelationProperties of rInterpretation of r
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What are the important topics in Linear Correlation for Gujarat Board Class 12 Statistics?
Key topics in Linear Correlation include Core Concepts and Definitions, Scatter Diagram Method, Karl Pearson's Product Moment Method, Properties of Correlation Coefficient – Detailed Study. Study these first, then practise questions on each for the Gujarat Board Class 12 board exam.
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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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