Final answer:
Switching the explanatory and response variables in a regression analysis significantly changes the least squares regression line because it alters the optimization problem of minimizing the sum of the squares of the residuals.
Step-by-step explanation:
Switching the explanatory and response variables in a regression analysis does indeed change the least squares regression line. For a given set of data, the regression line calculated with one variable as the independent variable and the other as the dependent variable will not be the same as the regression line calculated with the roles of the variables reversed. This is because the least squares method minimizes the sum of the squares of the vertical distances of the points from the line (the residuals) specifically for the chosen direction (predicting y from x, or vice versa).
When you change the roles of the explanatory and response variables, you are changing the axis with respect to which the residuals are measured and minimized, thereby creating a different optimization problem. Consequently, both the slope and the y-intercept of the regression line will generally be different. Therefore, the correct answer to the question is: A) Yes, it will change significantly.