Business Degree Certification Practice Test

What measure indicates how precise a prediction of Y is based on X?

1. Regression equation

2. Slope of the line

3. Standard error of estimate

4. Least squares principle

The correct answer is: Standard error of estimate

The standard error of estimate is a critical measure in regression analysis that quantifies how much the predicted values of Y deviate from the actual values. It essentially provides insight into the precision of the predictions made for Y based on the input variable X. A smaller standard error indicates that the predictions are closer to the actual data points, suggesting a more precise model. This measure helps in understanding the accuracy of the regression analysis; if the standard error is large, it indicates greater variability and less reliability in the predictions. In contrast, the regression equation outlines the relationship between the variables and serves as the mathematical model. While it provides a framework for understanding how changes in X affect Y, it does not directly indicate the precision of these predictions. The slope of the line is important as it reflects the rate of change of Y with respect to X; it is vital for understanding the direction and strength of the relationship but is not a direct measure of prediction precision. The least squares principle is a method used to determine the best-fitting line through the data points by minimizing the sum of the squares of the residuals. While it is foundational in creating the regression model, it does not provide a direct measure of prediction accuracy. Thus, the standard error of estimate specifically addresses the precision