What is the name of the equation represented as y^ hat = b0 + b1x1 + b2x2 + ... + bpxp?

The equation represented as ( \hat{y} = b_0 + b_1x_1 + b_2x_2 + ... + b_px_p ) is known as the Estimated Multiple Regression Equation. This equation is used in statistics to model the relationship between a dependent variable and multiple independent variables.

In this representation, ( \hat{y} ) is the predicted value of the dependent variable based on the input values of the independent variables ( x_1, x_2, ... , x_p ). The coefficients ( b_0, b_1, b_2, ..., b_p ) are estimated parameters obtained through statistical techniques that best fit the data. This is distinct from the population regression equation, which typically refers to the true relationship in the population rather than the estimated one derived from sample data.

The term "estimated" highlights that the parameters ( b_0, b_1, ... , b_p ) are not the actual population parameters but rather estimates based on the sampled data. This encapsulates the essence of regression analysis as it seeks to understand how changes in the independent variables influence the dependent variable through estimation rather than certainty.

Understanding this distinction is crucial in the context of regression analysis