Final answer:
The measure that reflects the precision of predictions of Y based on X is the standard error of estimate. It averages the distances between observed values and the regression line, providing an indicator of precision in the linear regression model. the correct option in the final answer is c) Standard error of estimate.
Step-by-step explanation:
The measure that indicates how precise a prediction of Y is based on X, or conversely, how inaccurate the prediction might be, is known as the standard error of estimate. This statistic gives us an idea of the average distance that the observed values fall from the regression line. Hence, a smaller standard error indicates a tighter cluster of points around the regression line, which implies more precise predictions.
The least squares principle is used to derive the best-fit line in linear regression by minimizing the sum of squared residuals or errors. The slope of the regression line indicates how much the dependent variable Y changes for a one-unit increase in the independent variable X. Despite being related, neither the slope nor the regression equation themselves are measures of precision or accuracy of the predictive relationship.
Therefore, the correct option in the final answer is c) Standard error of estimate.