Data Modelling
Data modelling involves selecting, fitting, and evaluating mathematical models (linear, quadratic, exponential) to represent and predict real-world data.
What You Need to Know
Key Concept Diagram
A linear model y = mx + b is used when data shows a constant rate of change
A quadratic model y = ax^2 + bx + c suits data with a single turning point
An exponential model y = ab^x suits data that grows or decays by a constant percentage
Residual plots help assess whether a model is appropriate
The coefficient of determination R^2 measures how well the model fits the data (0 to 1)
Key Vocabulary
Mathematical model
A mathematical description of a real-world situation
Residual plot
A graph of residuals against predicted values used to check model fit
Coefficient of determination
R^2, a measure of how well a regression model explains variation in the data
Extrapolation
Using a model to predict values outside the observed data range
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which model best suits data that doubles every year?
Question 2
An R^2 value of 0.95 means:
Question 3
A residual plot with a random scatter around zero indicates:
Key Concepts Summary
- ●A linear model y = mx + b is used when data shows a constant rate of change
- ●A quadratic model y = ax^2 + bx + c suits data with a single turning point
- ●An exponential model y = ab^x suits data that grows or decays by a constant percentage
- ●Residual plots help assess whether a model is appropriate
- ●The coefficient of determination R^2 measures how well the model fits the data (0 to 1)