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Class 12 Statistics Notes · GSEB

Meaning of Regression

Regression — learn the definition, dependent and independent variables, regression lines, and the equation Y = a + bX. GSEB Class 12 Statistics notes with key exam points.

Last updated: 22 Sep 2026

Notes

Meaning of Regression

Linear Regression — Chapter 1, GSEB Class 12 Statistics

What is Regression?

Regression
Regression is a statistical technique used to estimate the unknown value of one variable (dependent) based on the known value of another variable (independent). It finds the best-fit straight line through a scatter of points.

Regression = Drawing the Best-Fit Line

Known X

Input variable

Predict Y

Output variable

While correlation measures how strongly two variables are related, regression goes further — it gives us the equation to predict one from the other.

Dependent and Independent Variables

Dependent Variable (Y)

  • The variable we want to predict
  • Also called the regressand or response variable
  • Plotted on the vertical (Y) axis
  • Example: Marks (what we predict)

Independent Variable (X)

  • The variable we use to predict
  • Also called the regressor or explanatory variable
  • Plotted on the horizontal (X) axis
  • Example: Study hours (what we use to predict)
How to remember: Y depends on X. “Marks depend onstudy hours.” So marks = Y (dependent), study hours = X (independent).

Two Regression Lines

Since correlation is symmetric but regression is not, there are two separate regression lines:

Y on X (Primary)

Predicts Y from a given value of X

Example: “If study hours = 8, predict marks”

Used when X is known and Y is unknown

X on Y (Secondary)

Predicts X from a given value of Y

Example: “If marks = 85, predict study hours”

Used when Y is known and X is unknown

The Regression Equation

The regression line is a straight line described by:

Regression Equation (Y on X)

Y=a+bXY = a + bX

a = Intercept

Value of Y when X = 0

Where the line crosses the Y-axis

b = Slope

Change in Y per unit change in X

How much Y increases when X increases by 1

Example: If Y = 30 + 6.5X, then:
• When X = 0, Y = 30 (intercept)
• When X increases by 1, Y increases by 6.5 (slope)
• When X = 8 (study hours), Y = 30 + 6.5(8) = 82 (predicted marks)

Key Takeaways

Key Takeaways

  • Regression estimates the unknown value of one variable from the known value of another.
  • Dependent variable (Y) = what we predict; Independent variable (X) = what we use to predict.
  • There are two regression lines: Y on X (predict Y) and X on Y (predict X).
  • The regression equation Y = a + bX defines the best-fit straight line.
  • a (intercept) = Y value when X = 0; b (slope) = change in Y per unit change in X.
  • Regression goes beyond correlation — it gives us a prediction equation, not just a strength measure.