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Revision Notes
Linear Regression — Revision Notes
Gujarat Board · Class 12 · Statistics
Linear Regression revision notes for Gujarat Board Class 12 Statistics: 4 topics in quick points. Part of the Gujarat Board Class 12 Statistics syllabus.
17 formulas & key relations5 concepts
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Key Topics to Revise
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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.
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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.
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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.
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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).
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Full NotesKey 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?
Key topics in Linear Regression include Core Concepts: Regression vs. Correlation, Fitting the Regression Line – Method of Least Squares, Step-by-Step Worked Examples, Regression Coefficient – Properties and Interpretation. Study these first, then practise questions on each for the Gujarat Board Class 12 board exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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