Regression

 

What is Regression?

Regression is a statistical method used to examine the relationship between a dependent variable and one or more independent variables.

• It helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied.

• It is often used for prediction and forecasting.

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🔢 Types of Regression

Type	Description
Linear Regression	Models a straight-line relationship
Multiple Linear Regression	Uses more than one independent variable
Polynomial Regression	Fits a curve instead of a straight line
Logistic Regression	Used when the dependent variable is categorical
Ridge/Lasso Regression	Used when multicollinearity exists

📊 1. Simple Linear Regression

🔍 Goal:

Predict a continuous dependent variable using one independent variable.

🔢 Equation:

$$y = a + bx$$

Where:

• $y$ = dependent variable (output)

• $x$ = independent variable (input)

• $a$ = intercept (value of $y$ when $x = 0$)

• $b$ = slope (change in $y$ for a one-unit change in $x$)

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Example: Predict Student Marks from Study Hours

Hours Studied (x)	Marks Obtained (y)
2	50
4	60
6	65
8	70
10	85

You want to predict marks based on hours studied.

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✅ Regression Output (e.g., via Excel or Python):

After applying regression, you might get:

$$y = 45 + 4x$$

So, if a student studies 7 hours:

$$y = 45 + 4×7 = 73$$

🎯 Prediction: The student will score 73 marks.

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📊 2. Multiple Linear Regression

Used when more than one independent variable is used to predict a dependent variable.

🔢 Equation:

$$y = a + b_1x_1 + b_2x_2 + \dots + b_nx_n$$

 Example:

Predicting house price using:

• $x_1$: size of house (sq ft)

• $x_2$: number of bedrooms

$$\text{Price} = 50000 + 300×(\text{sq ft}) + 10000×(\text{bedrooms})$$

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📉 3.Logistic Regression (for classification)

Used when the output is categorical, like Yes/No, 0/1, True/False.

Example:

Predict whether a student passes (1) or fails (0) based on study hours.

Output: Probability → if above 0.5, we classify as "pass".