my goal is to create a ipynb file to learn about how to create a Linear Regression Model.

The problem:

1. How to set the initial w and b, should I set it randomly?
2. When to change the w or b on each iteration.
3. By how many should I update the w or b on each iteration.

Expected result:

1. there is a Model class with a __init__ and fit function.
2. the fit function will increment or decrement the w or b on each iteration.

What I’ve tried:

1. create the graph

plt.xlim(-2, 11)
plt.ylim(-2, 11)

x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
y = [-1, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9]
plt.plot(x, y, 'ro')

# y = x
x = [0,10]
y = [0,10]
plt.plot(x, y)

# fill_between
x = [0, 10]
y1 = [-1, 9]
y2 = [1, 11]
plt.fill_between(x, y1, y2, alpha=0.2)

del x, y

2. create a loss function.

# dots
x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
y = [-1, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9]

# calculated from y = 1x + 0
ŷ = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

# the loss function of linear regression is (ŷ - y)²
# other name is: the residual
def calculate_linear_regression_loss_function(ŷ: list[int], y: list[int]) -> list[int]:
  # map to numpy array (for syntatic sugar)
  np_ŷ = np.array(ŷ)
  np_y = np.array(y)
  # measure distance between ŷ and y
  distances = np_ŷ - np_y
  # square each distance
  squares = distances ** 2
  # sum the squares
  return squares.sum()

print(calculate_linear_regression_loss_function(ŷ, y))

del x, ŷ, y

3. create the generate training data function

def generate_training_data(n: int) -> list[list[int]]:
    training_data: list[list[int]] = []

    for _ in range(n):
        x = randrange(0, 1000) / 100
        y = randrange(0, 1000) / 100
        training_data.append([x, y])

    return training_data

generate_training_data(n=10)

def separate_training_data_into_x_y(training_data: list[list[int]]) -> tuple[list[int], list[int]]:
    array = np.array(training_data)
    return array[:,0], array[:, 1]

training_data = generate_training_data(n=10)
print("training_data", training_data)

x_training, y_training = separate_training_data_into_x_y(training_data=training_data)
print("x_training", x_training)

training_data = generate_training_data(10)
x_training, y_training = separate_training_data_into_x_y(training_data=training_data)

plt.plot(x_training, y_training, 'ro')