https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/regression-library/v/introduction-to-residuals-and-least-squares-regression 2022-10-07T00:58:19.561984208Z Introduction to residuals and least squares regression Introduction to residuals and least squares regression video https://cdn.kastatic.org/ka_thumbnails_cache/a2910682-b490-4ceb-83a9-b4e04af7fb1e_1280_720_base.png Introduction to residuals and least squares regression Introduction to residuals and least squares regression https://cdn.kastatic.org/ka-youtube-converted/yMgFHbjbAW8.mp4/yMgFHbjbAW8.mp4 460 Understanding regression model https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/regression-library/a/introduction-to-residuals 2023-02-22T03:54:13.328982673Z Introduction to residuals Build a basic understanding of what a residual is.  article https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/xfb5d8e68:residuals/v/calculating-residual-example 2023-12-15T19:01:48.939979194Z Calculating residual example We look at an example scenario that includes understanding least squares regression, interpreting the regression equation, calculating residuals, and interpreting the significance of positive and negative residuals in relation to the regression line. video https://cdn.kastatic.org/ka_thumbnails_cache/27a61578-a2f6-426c-a2c4-c1ebc921456b_1280_720_base.png Calculating residual example We look at an example scenario that includes understanding least squares regression, interpreting the regression equation, calculating residuals, and interpreting the significance of positive and negative residuals in relation to the regression line. https://cdn.kastatic.org/ka-youtube-converted/50ezMTE_BuA.mp4/50ezMTE_BuA.mp4 292 Understanding regression model https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/xfb5d8e68:residuals/e/calculating-interpreting-residuals 2022-06-10T19:18:02.50566201Z Calculating and interpreting residuals Practice calculating residuals in scatterplots and interpreting what they measure. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/least-squares-regression/v/calculating-the-equation-of-a-regression-line 2023-12-15T19:01:48.939979194Z Calculating the equation of a regression line We determine the correlation coefficient for bivariate data, which helps understand the relationship between variables. We then build the equation for the least squares line, using standard deviations and the correlation coefficient. The regression line equation y hat = mx + b is calculated. video https://cdn.kastatic.org/ka_thumbnails_cache/c8051e59-cfa8-46bf-9bea-212749b6d65b_1280_720_base.png Calculating the equation of a regression line We determine the correlation coefficient for bivariate data, which helps understand the relationship between variables. We then build the equation for the least squares line, using standard deviations and the correlation coefficient. The regression line equation y hat = mx + b is calculated. https://cdn.kastatic.org/ka-youtube-converted/FGesqq22TCM.mp4/FGesqq22TCM.mp4 491 Understanding regression model https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/least-squares-regression/e/calculating-equation-least-squares 2021-07-01T02:19:31Z Calculating the equation of the least-squares line Practice using summary statistics and formulas to calculate the equation of the least-squares line. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/least-squares-regression/v/interpreting-slope-of-regression-line 2023-12-15T19:01:48.939979194Z Interpreting slope of regression line We look at an example scatter plot showing the relationship between hours studying and test scores. We interpret scatter plots, investigate the relationship between variables, interpret the slope of a trend line, and make predictions based on the trend line's slope and intercept. video https://cdn.kastatic.org/ka_thumbnails_cache/99fc0bd7-0b3e-4634-94dc-23d54366b16a_1280_720_base.png Interpreting slope of regression line We look at an example scatter plot showing the relationship between hours studying and test scores. We interpret scatter plots, investigate the relationship between variables, interpret the slope of a trend line, and make predictions based on the trend line's slope and intercept. https://cdn.kastatic.org/ka-youtube-converted/PplggM0KtJ8.mp4/PplggM0KtJ8.mp4 178 Understanding regression model https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/least-squares-regression/v/interpreting-y-intercept-in-regression-model 2022-10-07T00:58:19.561984208Z Interpreting y-intercept in regression model Interpreting y-intercept in regression model video https://cdn.kastatic.org/ka_thumbnails_cache/0a7b8fc3-5598-4161-9892-b1f1cd89dc66_1280_720_base.png Interpreting y-intercept in regression model Interpreting y-intercept in regression model https://cdn.kastatic.org/ka-youtube-converted/00YVR5TSZqw.mp4/00YVR5TSZqw.mp4 156 Understanding regression model https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/v/interpreting-trend-line 2023-05-12T21:01:01.897246564Z Interpreting a trend line The graph shows how studying affects test scores. The line slope of 15 means that for each extra hour of studying, there is usually a 15-point increase in test score. But it's not a guarantee. Some students may do better or worse than the trend. Sal Khan video https://cdn.kastatic.org/googleusercontent/q6LtptyvaCJtK4B65rKXTxIBmuj58LNfXUvDVnBXexPpKLWuKR_luyJu8lkPcR8AVjDN0bE-8rHBTxpN9Zm7lrls Interpreting a trend line The graph shows how studying affects test scores. The line slope of 15 means that for each extra hour of studying, there is usually a 15-point increase in test score. But it's not a guarantee. Some students may do better or worse than the trend. https://cdn.kastatic.org/ka-youtube-converted/mfX_yUvwJho.mp4/mfX_yUvwJho.mp4 208 Understanding regression model https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-data/cc-8th-line-of-best-fit/e/interpreting-slope-and-y-intercept-of-lines-of-best-fit 2026-02-24T15:30:30.425876844Z Interpreting slope and y-intercept for linear models Practice explaining the meaning of slope and y-intercept for lines of best fit on scatter plots. Jeff exercise