Final answer:
A fitted value in a multiple regression model is the predicted value of the dependent variable given specific values for the independent variables, derived from the line of best fit calculated by minimizing the sum of squared residuals.
Step-by-step explanation:
A fitted value for a multiple regression model is the predicted value of the dependent variable based on the regression equation and the given values of the independent variables. This value is derived from the estimated equation of the line of best fit, usually found by the least-squares method, which minimizes the sum of squared residuals (errors).
These residuals are the differences between the actual values of the dependent variable in the dataset and the predicted values estimated by the regression line.
For example, considering the equation ŵ = -173.51 + 4.83x derived from sample data like the third exam (x value) versus the final exam score (y value), if we want to predict the final exam score based on a third exam score of 70, we would plug the value of 70 for 'x' into our equation to calculate the fitted value for 'y'.
The fitted value is used to make predictions within the range of the sample data but is not recommended for extrapolation beyond the observed data points due to potential inaccuracies that can arise.