Correlation and Regression

Name: Correlation and Regression
Author: StemPy Lab

Do students who sleep longer score higher? Does a hotter day sell more ice cream? A scatter plot shows the pattern, and the correlation coefficient puts a number on it. Then fit the line of best fit by least squares, in both directions, and use it to predict. You also learn when a prediction can be trusted, and the traps that catch many students: causation, outliers and going beyond the data. The Indian Class 11 and 12 mathematics books do not teach this topic. A-Level, IB, AP Statistics and the SAT do.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Scatter plots and the correlation coefficient
A scatter plot shows two measurements for each person or thing as one point. The correlation coefficient $r$ measures how closely the points follow a straight line, from $-1$ to $1$ . It says nothing about a curve, and it does not say that one quantity causes the other.
1 simulation1 practice question1 Python program4 problems
Read the lesson
Lesson 2about 25 min
The two regression lines
The regression line of $y$ on $x$ is the straight line that makes the sum of the squared vertical misses as small as possible. It always passes through the point of the two means. There is a second line, of $x$ on $y$ , and the product of the two slopes is $r^2$ .
1 simulation1 practice question1 Python program4 problems1 Python lab
Read the lesson
Lesson 3about 25 min
Prediction and the usual traps
A regression line is good for predicting inside the range of the data and poor outside it. $r^2$ tells the share of the variation that the line explains. One odd point can change a line, a strong correlation is not proof of cause, and a pattern that holds for each group can reverse when the groups are mixed.
1 simulation1 practice question1 Python program2 problems1 Python lab1 question set1 note
Read the lesson

Test Your Learning

Correlation and Regression: Chapter Test

20 questions · 50 min

Not started

Your teacher

StemPy Lab

← Statistics

← Comparing and Combining DataNext →

More onStatistics and Probability › Statistics

Discussion (0)

Loading…

Correlation and Regression

Course outline (3 lessons)

Scatter plots and the correlation coefficient

The two regression lines

Prediction and the usual traps

Test Your Learning

Your teacher

Discussion (0)