Online Robotics Classes for Kids in Vienna

1. Four-Step Implementation Workflow

1. Load data — input features (x) and targets (y)
2. Hypothesis — ŷ = mx + b
3. Cost — Mean Squared Error
4. Gradient descent — derivatives for m and b, then iterative updates

2. Math: Hypothesis, Error, Derivatives

Hypothesis: ŷ = mx + b. Error: ŷ − y. MSE = average of squared errors.

Partial derivatives:

• ∂J/∂m = (2/N) Σ (ŷ − y) · x — includes x because m multiplies x
• ∂J/∂b = (2/N) Σ (ŷ − y) — no x because b is independent of x

Updates: m_new = m_old − α · ∂J/∂m ; b_new = b_old − α · ∂J/∂b

3. Python Training Loop (Concept)

Initialize m = 0, b = 0, learning_rate = 0.01, epochs = 5. Each epoch:

1. y_pred = m * x + b
2. cost = mean((y_pred − y)²)
3. dm = (2/n) * sum((y_pred − y) * x); db = (2/n) * sum(y_pred − y)
4. m −= learning_rate * dm; b −= learning_rate * db
5. Log MSE, m, and b

4. Example Epoch Trace

Epoch	MSE	Slope m	Intercept b
1	18.00	0.27	0.09
2	11.10	0.47	0.14
3	7.08	0.62	0.19
4	4.73	0.74	0.22
5	3.37	0.83	0.26

Error falls steadily while m and b move toward a better fit — gradient descent is working as intended.

5. Line of Best Fit

The final line (e.g. y ≈ 0.83x + 0.26) follows the cloud of points. Real data rarely sits exactly on the line; residual distances remain. Gradient descent finds parameters that minimize total squared residual error.