Apply modelling to areas (financial forecasting, climate change)

What is Modelling?

Modelling is the process of creating a simplified representation of a real‑world system so we can analyse, predict, or control it. Think of it like building a miniature city: you don’t need every single street, but you include the main roads, parks, and key buildings to understand traffic flow or resource use. In IT, we use models to turn complex data into understandable patterns.

Why Modelling Matters in IT

• Helps predict future trends (e.g., stock prices, weather).
• Reduces risk by testing scenarios before real implementation.
• Improves decision‑making with visual and quantitative evidence.
• Facilitates communication between developers, analysts, and stakeholders.

Suppose a company wants to predict next year’s revenue based on the last five years of sales data. We can use a simple linear regression model:

$$\hat{y} = \beta_0 + \beta_1 x$$

Where y is revenue, x is time (year), β₀ is the intercept, and β₁ is the slope. By fitting the model to past data, we estimate β₀ and β₁ and then plug in x = 6 to forecast year 6 revenue.

Analogy: Think of the regression line as a straight road that best fits the curve of past sales. The farther you drive along this road, the better you can predict where you’ll end up.

Climate models simulate Earth’s atmosphere, oceans, and land surface to predict temperature changes. A common approach is the General Circulation Model (GCM), which solves equations for fluid dynamics and thermodynamics:

$$\frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot abla)\mathbf{v} = -\frac{1}{\rho}abla p + \mathbf{g} + \mathbf{F}_{\text{visc}}$$

Here, v is wind velocity, ρ density, p pressure, g gravity, and F_visc viscous forces. By running the model with different greenhouse gas scenarios, scientists can estimate future temperature rises.

Analogy: Imagine a giant, super‑powerful blender mixing air, water, and land. The model tells us how the mixture will change over time.

Key Points to Remember

• Always define the model’s purpose (prediction, explanation, optimisation).
• Check assumptions: linearity, independence, normality.
• Use appropriate evaluation metrics: RMSE for regression, R² for fit.
• Explain the model’s limitations and potential bias.

Sample Question

“Explain how you would use a linear regression model to forecast next year’s sales for a company that has recorded the following revenue (in £k) over the last five years: 120, 135, 150, 165, 180. Show your calculations and discuss any assumptions.”

Answer Strategy

1. Plot the data and observe a clear upward trend.
2. Fit the regression line: compute β₀ and β₁ using least squares.
3. Predict for year 6 (x=6).
4. State assumptions: linearity, constant variance, no outliers.
5. Discuss model fit (e.g., R² ≈ 0.99).