Study of Models (UID : 1)

California Housing Price Prediction

Overview

This project presents a complete Exploratory Data Analysis (EDA) and Multiple Linear Regression modeling workflow using the California Housing dataset.
The task simulates a real-world Data Analyst role in a US Real Estate firm, focusing on data understanding, visualization, dimensionality reduction, and predictive modeling.

The implementation is done using Python, pandas, matplotlib, seaborn, and scikit-learn in a Jupyter Notebook.

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Dataset Description

The dataset contains information about housing blocks in California.

Feature	Description
longitude	How far west a house is (higher = farther west)
latitude	How far north a house is (higher = farther north)
housingMedianAge	Median age of houses in a block
totalRooms	Total rooms in a block
totalBedrooms	Total bedrooms in a block
population	Population in a block
households	Number of households in a block
medianIncome	Median household income (in tens of thousands USD)
medianHouseValue	Median house value (target variable)
oceanProximity	Proximity of houses to the ocean

Note: Due to temporary access issues with sklearn.datasets.fetch_california_housing, the dataset was downloaded manually and loaded locally.

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Objectives

• Perform thorough data exploration and understanding
• Analyze skewness and outliers
• Study feature correlations
• Apply Principal Component Analysis (PCA)
• Build a Multiple Linear Regression model
• Evaluate the model using multiple performance metrics
• Interpret model strengths and limitations

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Steps Performed

Data Loading & Basic Exploration

• Loaded dataset using pandas
• Displayed:
  • Dataset shape
  • Column names
  • First 10 rows
• Used .info() and .describe() to understand structure and statistics
• Identified missing values in totalBedrooms
• Computed feature variances to find the largest variance feature

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Univariate Analysis (Histograms)

• Plotted histograms for all numeric features
• Experimented with different bin sizes
• Observed right-skewed distributions in:
  • medianIncome
  • totalRooms
  • population

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Outlier Detection (Box Plots)

• Used box plots to detect outliers in:
  • medianIncome
  • averageRooms
  • population
• Identified several high-value outliers affecting distributions

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Correlation Analysis

• Computed correlation matrix
• Visualized correlations using a heatmap
• Used correlation insights for feature selection
• Observed weak linear correlation of latitude and longitude with house prices

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Geographical Visualization

• Scatter plot:
  • Longitude vs Latitude
• Color mapped by Median House Value
• Point size scaled by Population
• Revealed higher house prices near coastal regions

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Principal Component Analysis (PCA)

PCA Workflow

• Standardized features
• Applied PCA
• Plotted Explained Variance Ratio (Scree Plot)
• Selected top 2 principal components
• Scatter plot of PC1 vs PC2, colored by house value

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Multiple Linear Regression Model

• Built a scikit-learn Pipeline including:
  • Feature scaling
  • Linear Regression
• Excluded latitude and longitude based on correlation analysis
• Extracted:
  • Regression coefficients
  • Intercept

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Model Evaluation

Model performance was evaluated using:

• Mean Squared Error (MSE)
• Mean Absolute Error (MAE)
• R² Score

Questions

• Q.1)Explain most widely used methods to eliminate skewness of column features
• Q.2) Why Scaling is Required Before PCA?
• Q.3) Is high R2 score always good?
• Q.4) Is low training loss always preferred?

all above questions answers given in jupyter notebook

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Diagnostic Plots

• Predicted vs Actual values
• Residuals vs Predicted values
  • Reveals limitations of linear regression

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