Malaysian House Price Index Prediction

Linear Algebra Group Project

Predicting the Malaysian House Price Index (MHPI) using two linear algebra techniques: Least Squares Regression and Discrete Dynamical Systems. Data spans 2010–2023.

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Problem Statement

Housing affordability is a growing concern in Malaysia. This project uses macroeconomic indicators to model and forecast the MHPI, answering: which economic factors drive house prices, and where are prices headed?

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Dataset

14 years of annual data (2010–2023), compiled from official Malaysian sources:

Variable	Source	Range
price_index	MHPI (Bank Negara / NAPIC)	100.0 – 218.3
Population_000s	DOSM Malaysia	28,589 – 33,402 (thousands)
GDP_RM_Million	DOSM (2010–2014 back-calculated)	RM 1.82M – RM 3.14M million
OPR_Rate_Percentage	Bank Negara Malaysia	1.75% – 3.25%

GDP for 2010–2014 was back-calculated from the 2015 base using official BNM annual growth rates.

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Methods

1. Least Squares Regression (LSR)

Fits a multi-variable linear model using the normal equation:

$$\mathbf{x} = (\mathbf{A}^T \mathbf{A})^{-1} \mathbf{A}^T \mathbf{b}$$

Model equation (standardized):

Price Index = 170.06 + 33.28(Population) + 3.37(GDP) - 1.30(OPR Rate)

Results:

• R² = 0.9975 (explains 99.75% of variance)
• RMSE = ±1.86 index points
• Population is the strongest predictor (r = 0.998)

2. Discrete Dynamical System (DDS)

Models price as a sequential process — next year's price depends on this year's:

$$P_{t+1} = aP_t + b$$

Fitted equation:

P_{t+1} = 0.9098 × P_t + 24.11

Results:

• R² = 0.9936
• RMSE = ±2.61 index points
• Growth factor |a| < 1 → stable system, converges to equilibrium P* ≈ 267.20
• Forecast: MHPI reaches ~233.7 by 2027

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Key Findings

• MHPI grew 118.3% from 2010 to 2023 (~8.45%/year average)
• Population is the dominant driver (r = 0.998 with MHPI)
• OPR Rate has a negative relationship — higher interest rates suppress prices
• Both models agree the system is stable and converging toward ~267 index points
• LSR is better for causal explanation; DDS is better for standalone forecasting

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Files

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├── analysis.ipynb          # Main notebook — all analysis, plots, and results
├── gdp_back-caclulate.py   # Data prep script — merges population, GDP, OPR data
├── project_final_data.csv  # Final cleaned dataset used in analysis
├── gdp_state_real_supply.csv
├── opr-decision.csv
├── population_malaysia.csv
└── Table MHPI 2024P.xlsx   # Raw MHPI data from NAPIC

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How to Run

# Install dependencies
pip install pandas numpy matplotlib seaborn scipy

# Run data prep (if regenerating project_final_data.csv)
python gdp_back-caclulate.py

# Open the main analysis
jupyter notebook analysis.ipynb

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Tech Stack

• Python 3
• NumPy (matrix operations, normal equations)
• Pandas (data wrangling)
• Matplotlib / Seaborn (visualizations)
• SciPy (Q-Q plots, distribution checks)