Introduction to Regression Analysis 📉
Regression Analysis is a powerful statistical tool used to estimate the relationship between two or more variables. It helps in predicting the value of one variable based on the value of another.
Analysis Workflow 🔄
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What is Regression? 🤔
[!NOTE] Definition: Regression is the measure of the average relationship between two or more variables in terms of the original units of the data.
Origin: The term "Regression" was first used by Sir Francis Galton in 1877 while studying the relationship between the heights of fathers and sons.
In simpler terms, if two variables are correlated, regression allows us to predict the unknown value of one variable from the known value of the other.
Purpose & Utility of Regression 🎯
- Estimation & Prediction: The primary use is to estimate the value of the dependent variable for a given independent variable.
- Example: Predicting sales based on advertising expenditure.
- Nature of Relationship: It tells us the nature of the relationship (positive or negative) between variables.
- Measure of Error: It helps in calculating the error involved in estimating the values.
- Policy Making: Governments and businesses use it to formulate policies based on future predictions (e.g., population growth, tax revenue).
Key Terms 🗝️
- Independent Variable (X): The variable which is used to predict. Also called the Explanatory or Predictor variable.
- Dependent Variable (Y): The variable which is to be predicted. Also called the Explained or Response variable.
| Variable | Symbol | Role |
|---|---|---|
| Independent | X | The Cause (Predictor) |
| Dependent | Y | The Effect (Predicted) |
Example Scenario 🏪
Imagine a coffee shop owner wants to know how temperature affects coffee sales.
- Temperature (X): Independent Variable (We know this).
- Coffee Sales (Y): Dependent Variable (We want to predict this).
By analyzing past data using regression, the owner can predict: "If the temperature drops to 10°C, how many cups will I sell?"
Summary
- Regression goes a step beyond correlation. While correlation gives the degree of relationship, regression gives the functional relationship.
- It is the "Line of Best Fit" that minimizes the error in prediction.
- Widely used in business, economics, and social sciences for forecasting.
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