Linear Regression — Chapter Summary
Gujarat Board · Class 12 · Statistics
Summary of Linear Regression for Gujarat Board Class 12 Statistics. Part of the Gujarat Board Class 12 Statistics syllabus.
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Overview
Linear Regression is a powerful statistical tool that extends the concept of correlation by establishing a functional (mathematical) relationship between two correlated variables. While correlation tells us the strength and direction of a relationship, regression allows us to predict or estimate the
Key Concepts
Regression means 'to return to
Regression means 'to return to the mean value'. The term was coined by Sir Francis Galton while studying heights of fathers and sons. He observed that
In any cause
In any cause-effect relationship: X = Independent / Explanatory Variable (the cause; the variable whose value is known). Y = Dependent / Explained Var
The linear regression model
The linear regression model is: Y = a + bX + ε. Where: Y = Dependent Variable, X = Independent Variable, a = Constant (intercept), b = Constant (regre
Steps
Steps: (1) Plot all n ordered pairs (xᵢ, yᵢ) on a graph to form a scatter diagram. (2) Draw a line that passes as close as possible to all the plotted
The best
The best-fitted regression line Ŷ = a + bX is obtained by minimising Σeᵢ² = Σ(yᵢ – ŷᵢ)², the sum of squares of errors. The error eᵢ = yᵢ – ŷᵢ (positiv
Learning Objectives
- Understand the meaning, origin, and concept of linear regression and how it differs from correlation
- Distinguish between independent (explanatory) variable X and dependent (explained) variable Y
- Learn the Linear Regression Model: Y = a + bX + ε
- Fit a regression line using the Method of Scatter Diagram and the Method of Least Squares
- Compute regression coefficient b and intercept a using direct and short-cut methods
Frequently Asked Questions
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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