Regression

Fit continuous targets with gradient descent and inspect residual behavior visually.

Interactive simulation

Line fitting + loss minimization

True slope1.20

True intercept0.40

Noise level0.20

Learning rate0.08

GD steps60.00

Learned slope

1.157

Learned intercept

0.402

MAE

0.126

RMSE

0.142

Chart

Mathematical intuition

OLS objective

\min_{m,b}\;\frac{1}{N}\sum_{i=1}^N(y_i-(mx_i+b))^2

Gradient descent repeatedly moves parameters against the gradient to lower this loss.

Step-by-step workflow

Input → Processing → Learning → Prediction → Output

Input

Feature x and target y

Processing

Forward pass: yhat = mx+b

Learning

Compute gradient and update

Prediction

Apply learned line

Output

Continuous value

Code implementation

Python gradient descent

python

m, b = 0.0, 0.0
for _ in range(steps):
    dm = db = loss = 0.0
    for x, y in data:
        yhat = m*x + b
        err = yhat - y
        loss += err**2
        dm += err*x
        db += err
    dm = 2*dm/len(data)
    db = 2*db/len(data)
    m -= lr*dm
    b -= lr*db

Loading Lab...

m, b = 0.0, 0.0 for _ in range(steps): dm = db = loss = 0.0 for x, y in data: yhat = m*x + b err = yhat - y loss += err**2 dm += err*x db += err dm = 2*dm/len(data) db = 2*db/len(data) m -= lr*dm b -= lr*db