回帰分析Regression analysis

Learn in the textbookStatistical Analysis and Inference

DefinitionRegression analysis (回帰分析) is an analysis method that expresses the relationship between a target variable and explanatory variables as a regression equation (回帰式), and uses the explanatory variable values to predict the target variable.

ExplanationWith one explanatory variable it is called simple regression analysis (単回帰分析), and with two or more it is called multiple regression analysis (重回帰分析). Simple regression finds the straight line y = ax + b that best fits the dots on a scatter plot and uses it for prediction.

AnalogyIt is like drawing a single path through scattered footprints, then following that path to guess where the next step will land.

Memory hookThe name "regression" comes from a study of parents' and children's heights, which found that children's heights tend to move back (regress) toward the average.

Learn in the textbookRegression, Correlation, and Spurious Correlation

DefinitionRegression analysis (回帰分析) expresses the relationship between variables as a formula so that the value of one variable can be explained or predicted from the values of one or more explanatory variables.

ExplanationThe variable used as the clue for prediction is the explanatory variable (説明変数), and the one being predicted is the target variable (目的変数). With a single explanatory variable and a straight-line relationship (y = a + bx) it is simple regression analysis (単回帰分析), and with several explanatory variables it is multiple regression analysis (重回帰分析).

AnalogyIt is like turning your past records of walking steps and calories burned into a quick reference chart, then using tomorrow's planned step count to estimate the calories you will burn.

Memory hookThe name comes from Galton's study showing that even when parents are unusually tall or short, their children's heights tend to "regress" toward the average.