In regression, what does Y-hat (Y^) represent?

In regression, what does Y-hat (Y^) represent?

• A. The actual observed value of Y.
• B. The intercept.
• C. The slope of the line.
• D. The predicted value of Y.

Answer: (B)

In regression, Y-hat is the predicted value of the dependent variable for the given predictor values. It’s the point on the regression line that corresponds to a particular X (or set of Xs) and represents the model’s estimate of what Y would be on average, given those inputs. It’s calculated from the regression equation, for example Ŷ = β0 + β1X in simple linear regression (and Ŷ = β0 + β1X1 + β2X2 + ... in multiple regression). The actual observed Y can differ from this prediction; that difference is the residual or error. The intercept and slope are the model’s parameters that define the line, not the predicted value itself.

In regression, Y-hat is the predicted value of the dependent variable for the given predictor values. It’s the point on the regression line that corresponds to a particular X (or set of Xs) and represents the model’s estimate of what Y would be on average, given those inputs. It’s calculated from the regression equation, for example Ŷ = β0 + β1X in simple linear regression (and Ŷ = β0 + β1X1 + β2X2 + ... in multiple regression). The actual observed Y can differ from this prediction; that difference is the residual or error. The intercept and slope are the model’s parameters that define the line, not the predicted value itself.