Linear regression and correlation

14 videos
3 skills
Even when there might be a rough linear relationship between two variables, the data in the real-world is never as clean as you want it to be. This tutorial helps you think about how you can best fit a line to the relationship between two variables.

Correlation and causality

VIDEO 10:45 minutes
Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise)

Fitting a line to data

VIDEO 7:48 minutes
Sal creates a scatter plot and then fits a line to data on the median California family income.

Estimating the line of best fit exercise

VIDEO 1:17 minutes
Sal solves a problem where he has to estimate the line of best fit for a scatter plot.

Eyeballing the line of best fit

PRACTICE PROBLEMS
Given a random assortment of points, draw a line of best fit through them.

Estimating slope of line of best fit

PRACTICE PROBLEMS
Given a scatter plot, can you estimate the slope of the line of best fit that goes through the data points?

Squared error of regression line

VIDEO 6:47 minutes
Introduction to the idea that one can find a line that minimizes the squared distances to the points

Proof (part 1) minimizing squared error to regression line

VIDEO 10:35 minutes
Proof (Part 1) Minimizing Squared Error to Regression Line

Proof (part 2) minimizing squared error to regression line

VIDEO 9:54 minutes
Proof Part 2 Minimizing Squared Error to Line

Proof (part 3) minimizing squared error to regression line

VIDEO 10:54 minutes
Proof (Part 3) Minimizing Squared Error to Regression Line

Proof (part 4) minimizing squared error to regression line

VIDEO 4:18 minutes
Proof (Part 4) Minimizing Squared Error to Regression Line

Regression line example

VIDEO 9:27 minutes
Regression Line Example

Second regression example

VIDEO 9:15 minutes
Second Regression Example

R-squared or coefficient of determination

VIDEO 12:41 minutes
R-Squared or Coefficient of Determination

Example: Correlation coefficient intuition

VIDEO 7:21 minutes
Sal explains the intuition behind correlation coefficients and does a problem where he matches correlation coefficients to scatter plots.

Correlation coefficient intuition

PRACTICE PROBLEMS
Match correlation coefficients to scatterplots to build a deeper intuition behind correlation coefficients.

Calculating R-squared

VIDEO 9:45 minutes
Calculating R-Squared to see how well a regression line fits data

Covariance and the regression line

VIDEO 15:08 minutes
Covariance, Variance and the Slope of the Regression Line