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Linear regression and correlation

13 videos
2 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

Estimating the line of best fit

PRACTICE PROBLEMS
Given a random assortment of points, find the best fit line for them.

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

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