Answer to Question #138211 in Statistics and Probability for jse

Question

1. What is Regression Analysis?
2. What is a Least-Squares Line?

Answer 1

1) Regression analysis is a well-known statistical learning technique useful to infer the relationship between a dependent variable Y and p independent variables X=[X₁|…|X_p]. The dependent variable Y is also known as response variable or outcome, and the variables X_k (k=1,…,p) as predictors, explanatory variables, or covariates. 

2) The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It's called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).