The Least-Squares Line

Name: The Least-Squares Line
Author: StemPy Lab

A school canteen sells more cold drinks on hot days.

How many should it order for tomorrow, when the forecast says 27 degrees?
Draw a straight line through the cloud of points and read off a prediction.
Learn which line fits best and why, what its slope and intercept say in words, and how the leftovers, the residuals, tell you when to trust it.

3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson

Course outline (3 lessons)

Lesson 1about 25 min
The line that fits best
A straight line through a scatter plot lets us predict. But which line? This lesson measures how far each point misses a line, its residual, and explains why the best line makes the sum of the squared residuals as small as possible.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 30 min
Slope, intercept and prediction
The least-squares line has a simple recipe: the slope is $r$ times the ratio of the standard deviations, and the line passes through the point of the means. This lesson builds the line, reads its slope and intercept in words, and shows why a prediction far outside the data can be nonsense.
1 simulation1 practice question1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Residuals and r squared
Residuals are the leftovers after the line has done its work. Plotted against $x$ , they show whether a straight line was the right choice. This lesson reads residual plots and introduces $r^2$ , the share of the variation in $y$ that the line accounts for.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
Read the lesson

10 questions · 20 min

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