Coding Grandmaster · project 37 of 46 · premium, free for now

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.

Learn

Machine learning starts with a model: a rule that turns an input into a prediction. The simplest is a straight line, prediction = m × x + b. To judge a model, measure its error. The mean squared error (MSE) averages the squared gaps between predictions and the true answers; squaring stops positive and negative gaps cancelling and punishes big misses. Training means finding the m and b with the smallest error.

Your task

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.

Stretch challenge

Try different m and b by hand to push the error below 100.

← Capstone: a report table Training by searching →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

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 →40

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.

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 Estimation Station

Estimate big sums without a calculator and see how close you get.

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FAQ

Predictions and error: common questions

I am stuck. What can I do?

Press Hint for a nudge, read the message next to each goal, and compare your code with the lesson text. If you still need it, Show answer reveals a model solution. Try to type it yourself rather than copy it.

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