If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Skip to main content
Subjects
  • Math by subject
    • Early math
    • Arithmetic
    • Algebra
    • Geometry
    • Trigonometry
    • Statistics & probability
    • Calculus
    • Differential equations
    • Linear algebra
    • Math for fun and glory
  • Math by grade
    • K–2nd
    • 3rd
    • 4th
    • 5th
    • 6th
    • 7th
    • 8th
  • Science & engineering
    • Physics
    • Chemistry
    • Organic chemistry
    • Biology
    • Health & medicine
    • Electrical engineering
    • Cosmology & astronomy
  • Computing
    • Computer programming
    • Computer science
    • Hour of Code
    • Computer animation
  • Arts & humanities
    • Art history
    • Grammar
    • Music
    • US history
    • World history
  • Economics & finance
    • Microeconomics
    • Macroeconomics
    • Finance & capital markets
    • Entrepreneurship
  • Test prep
    • SAT
    • MCAT
    • GMAT
    • IIT JEE
    • NCLEX-RN
    • CAHSEE
  • College Admissions
    DonateSign in / Sign up
    Search for subjects, skills, and videos
    Main content
    Statistics and probability Describing relationships in quantitative data
    Residuals, least-squares regression, and r-squared
    Introduction to residuals
    Squared error of regression line
    Regression line example
    Second regression example
    Proof (part 1) minimizing squared error to regression line
    Proof (part 2) minimizing squared error to regression line
    Proof (part 3) minimizing squared error to regression line
    Proof (part 4) minimizing squared error to regression line
    R-squared or coefficient of determination
    Calculating R-squared
    Covariance and the regression line
    Current time:0:00Total duration:10:35
    0 energy points
    Statistics and probability
    |Describing relationships in quantitative data|
    Residuals, least-squares regression, and r-squared

    Proof (part 1) minimizing squared error to regression line

    About
    Proof (Part 1) Minimizing Squared Error to Regression Line. Created by Sal Khan.
    ShareTweetEmail
    Residuals, least-squares regression, and r-squared
    Introduction to residuals
    Squared error of regression line
    Regression line example
    Second regression example
    Proof (part 1) minimizing squared error to regression line
    Proof (part 2) minimizing squared error to regression line
    Proof (part 3) minimizing squared error to regression line
    Proof (part 4) minimizing squared error to regression line
    R-squared or coefficient of determination
    Calculating R-squared
    Covariance and the regression line
    Tags
    Linear regression (least squares regression)
    Second regression example
    Proof (part 2) minimizing squared error to regression line
    Up Next
    Proof (part 2) minimizing squared error to regression line