8.3 Examples of Categorical Variables

Baseline Model: Manjula Nayak's Household Survey

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Regression Results:

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Adding Ownership as a Categorical Variable

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Adding Location as a Categorical Variable

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Baseline Model

Initial Model:

• Dependent variable (y): Selling price (in lakhs).
• Independent variable (x1): Area (in square feet).
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Limitations:

• Adding quantitative variables (e.g., bedrooms, bathrooms) led to multicollinearity issues, as these variables were highly correlated with area.

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Step 1: Adding a Categorical Variable (Premium Location)

New Model:

• Dependent variable (y): Selling price.
• Independent variables:
• x1: Area (quantitative).
• x2: Premium location (categorical; x2 = 1 for premium, x2 = 0 otherwise).

Regression Equation:

Results:

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Step 2: Adding Multiple Categorical Variables

Additional Variables:

• x3: Amenities (1 if present, 0 otherwise).
• x4: Gated community (1 if gated, 0 otherwise).

New Model:

• Regression equation:

Results:

• Enhanced model fit and reduced residuals.

Significance Tests:

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Residual Analysis

1. Standardized Residuals:

• No values exceeding ±3.
• Adding categorical variables improved the fit.

2. Plots of Residuals:

• Residuals vs. independent variables Random distribution, no patterns, indicating no bias.
• Residuals vs. predicted values Equally distributed above and below the x-axis.

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