Which of these is a coefficient estimated by a linear regression?

In the context of linear regression, the intercept is a crucial component of the estimated equation that describes the relationship between the independent (predictor) variables and the dependent (response) variable. Specifically, the intercept represents the expected value of the dependent variable when all independent variables are equal to zero. It essentially shifts the regression line up or down along the y-axis.

In linear regression analysis, various coefficients are estimated, and these include the slope coefficients for each predictor variable and the intercept. The slope coefficients indicate the change in the dependent variable for a one-unit change in an independent variable, whereas the intercept provides a baseline level of the dependent variable.

The other concepts mentioned, such as residual, squared error, and correlation, serve different purposes within the framework of regression analysis. Residuals are the differences between observed and predicted values, squared error is a metric used to evaluate how well the model fits the data, and correlation describes the strength and direction of the linear relationship between two variables but does not represent a coefficient estimated in the regression model itself. Thus, the intercept is indeed the coefficient estimated by a linear regression.