L19

08/10/26 Thu 8:02am

Data-Based Modelling

The process of developing a model of a system using measured data. The model learns relationship and pattern from the data to predict output or describe system behaviour.

graph TD
    A[Data based modelling] --> B[Supervised modelling]
    A --> C[Unsupervised]
    A --> D[system identification]
    
    B --> E[Regression]
    B --> F[Classification]
    
    C --> G[Clustering]
    G --> H[Silhouette Distance]

Regression	Classification
MSE	Confusion matrix
RMSE	→ Precision recall
IAE	→ Accuracy
$R^2$	→ F1 score

Linear Regression

$$y=mx+c$$ $$m=\frac{\text{Sum of production of deviation}}{\text{Sum of square of deviation for x}}$$ $$c=\text{mean of y}-(m\times \text{mean of x})$$

example:

V (x)	$\omega$ (y)	Mean of X	Mean of Y	Deviation in X	Deviation in Y	product of deviations	deviation of $x^2$
2	210	5	500	-3	-290	870	9
4	390	5	500	-1	-110	110	1
6	610	5	500	1	110	110	1
8	790	5	500	3	290	870	9
---	---	---	---	---	---	1960	20
now

$$m=\frac{\text{Sum of production of deviation}}{\text{Sum of square of deviation for x}}$$ $$\therefore m=\frac{1960}{20}=98$$ $$c=\text{mean of y}-(m\times \text{mean of x})$$ $$\therefore c=500-(98\times 5)=10$$

Now using the equation.

$$\hat{\omega }=98V+10$$

V(X)	$\omega$ (Y)	$\hat{\omega }$	$\omega -\hat{\omega }$ Error	Error Square
2	210	206	4	16
4	390	402	-12	144
6	610	598	12	16
8	790	794	-4	144
now Mean Squared Error is

$$MSE=\frac{1}{n}\sum _{i=1}^n\text{Error Square}$$