Final answer:
The statement is false. A simple regression line is used to predict the dependent variable (y) based on the independent variable (x), not the other way around. The least-squares regression line is used for predicting y within the data's range.
Step-by-step explanation:
The statement that a simple regression line can be used to predict values for the independent variable X is false. In simple linear regression, the regression equation is of the form y = a + bx, where y is the dependent variable we are trying to predict, a is the y-intercept, b is the slope, and x is the independent variable used to make predictions about y. The purpose of a regression line is to predict the dependent variable given the independent variable, not the other way around.
For example, if we are studying the relationship between a person's height (dependent variable y) and their pinky finger length (independent variable x), we would use the regression line to estimate someone's height given their pinky finger length, not to estimate pinky finger length from their height.
The least-squares regression line minimizes the residuals, which are differences between the actual data points and the predicted values on the line. This process ensures that the sum of squared errors is minimized, providing the best possible linear prediction for the data set at hand. However, it's important to recognize that predictions should generally not be made for values of x that fall outside the range of the data used to create the regression model, as the relationship may not hold outside that range. The prediction of y using the regression line is subject to the condition that there is a significant correlation between x and y.