Final answer:
The mean squared error is the error function that would result in the same slope and intercept values in linear regression analysis as using the RMSE. The slope and y-intercept of the regression line are found by minimizing the SSE of the best fit line, and the regression line's fit can be evaluated by looking at the coefficient of determination and the residuals.
Step-by-step explanation:
The question pertains to the selection of an error function in linear regression that would result in the same slope and intercept values as using the Root Mean Squared Error (RMSE). Of the options given, (a) Mean absolute error, (b) Mean squared error, (c) Mean percentage error, (d) Root mean squared error, the correct answer is (b) Mean squared error, because it is directly associated with the least-squares criteria for the line of best fit used in linear regression.
The slope and y-intercept of the regression line are determined by minimizing the Sum of Squared Errors (SSE), which is what the least-squares regression line accomplishes. The slope represents the rate at which the dependent variable changes for each unit change in the independent variable, while the y-intercept is the value of the dependent variable when the independent variable is zero.
The fit of the regression line is generally assessed using the coefficient of determination (r^2), which indicates how much of the variability in the response variable is explained by the linear model. A residual is the difference between an observed value and the value predicted by the regression line; it is used to identify outliers or influential points.