8.1.1 MLR: Categorical Variables

MLR Review

• Definition: A model predicting a dependent variable y using multiple independent variables

• Extension: In this module, categorical (qualitative) variables are introduced as independent variables alongside quantitative variables.

• Example: Flat prices might depend not only on area (quantitative) but also on whether the location is premium or not (categorical).

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Why Include Categorical Variables?

• Improved Predictions: Categorical variables often provide crucial context not captured by quantitative data.
• Example: In Mysuru flat price data:
  • Quantitative variables: Area, bathrooms, bedrooms.
  • Missing categorical variables: Amenities, apartment type, premium location.

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Handling Categorical Variables

• Key Concept: Categorical variables need to be converted into numerical form (dummy variables) for regression.
• Dummy Variables: Binary variables (0 or 1) representing categories.
• Example: Brand variable in Basavaraja's dataset.
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Steps in MLR with Categorical Variables

Model Formulation:

• Basic regression equation:

• x1​: Price (quantitative).

• x2: Brand (categorical, represented as dummy variable).

Data Analysis:

• Include both x1 and x2​ in the regression model.
• Use tools like Excel's Analysis ToolPak to calculate coefficients, , standard error, and ANOVA table.

Example Calculation:

• Basavaraja's dataset: Satisfaction score depends on:
• Price (x1): Quantitative.
• Brand (x2): Lenovo (1) or Dell (0).
• Regression Equation:

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Results and Interpretations

Performance Improvement:

• improved from 0.31 (price only) to 0.45 (price + brand).
• Standard error reduced from 5.19 to 4.85.

Significance Tests:

• F-test (overall significance):
• Null hypothesis: No linear relationship.
• F-statistic: 13.75 (p-value close to 0). Reject null hypothesis, indicating the model is significant.
• T-tests (individual significance):

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  • Price significantly influences satisfaction score.

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  • Brand also significantly impacts satisfaction.

Adding categorical variables (e.g., brand):

• Enhances the model's explanatory power and predictive accuracy.
• Interpretation of coefficients:
• β1: Satisfaction score increases by 1.29 units for every 1-lakh increase in price.
• β2: Lenovo users score 3.93 units higher than Dell users, on average.

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Simplified Explanation

What is Multiple Linear Regression (MLR)?

• It's like finding a formula to predict something (e.g., satisfaction score) using several factors (e.g., price, brand).

What’s New?

• Previously, we only used numbers (e.g., price).
• Now, we also include labels like brand (Lenovo, Dell) by turning them into numbers (dummy variables: 1 or 0).

Why Do This?

• Labels (categories) can also influence predictions. Including them improves accuracy.

How Do We Use It?

• Example:
• Satisfaction = 46.83 + (1.29 x price) + (3.93 x brand).
• If it’s Lenovo, brand = 1.
• If Dell, brand = 0.

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