Coding Grandmaster · project 40 of 46 · premium, free for now

The straight-line formula

Compute the slope and intercept with these formulas, print them rounded to 3 decimal places, and print the prediction for new_x rounded to 2 places.

Learn

For a line with a slope and an intercept, mathematicians solved training exactly. The best slope is the sum of (x − mean x) × (y − mean y) divided by the sum of (x − mean x)². The best intercept then makes the line pass through the point of the two means: b = mean y − slope × mean x. No searching, just arithmetic; this is ordinary least squares.

Your task

Compute the slope and intercept with these formulas, print them rounded to 3 decimal places, and print the prediction for new_x rounded to 2 places.

Stretch challenge

Check that gradient descent on the same data finds almost the same line.

← Gradient descent Classifying by neighbours →

Python

Press Run to see what your program prints.

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Predictions and error

Write predict(x, m, b) and mse(xs, ys, m, b). Print the prediction for each size and the mean squared error of the line with the given m and b, rounded to 2 decimal places.

Start →38

Training by searching

Try every m from 0 to 100 in steps of 5 and every b from 0 to 200 in steps of 10 with the same data. Print the best m, the best b and their error rounded to 2 decimal places.

Start →39

Gradient descent

Starting from m = 0, repeat steps times: compute the gradient, then do m = m - lr * gradient. Print the final m rounded to 4 decimal places and the final mean squared error rounded to 4.

Start →41

Classifying by neighbours

Write classify(point, train, k): sort the training examples by distance to the point, take the k closest, and return the label that appears most among them (if tied, the label of the nearest one).

Start →42

A perceptron learns AND

Train a perceptron on the AND truth table starting from zero weights, for the number of epochs, with each update using a learning rate of 1. Print the final weights and bias as w1 w2 b, then the four predictions.

Start →

Practise the idea

⚙️ Play Function Machine

Feed numbers into a mystery machine, plot what comes out, then crack its secret rule.

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FAQ

The straight-line formula: common questions

I am stuck. What can I do?

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