You have carried out a regression analysis but after thinking about the relationship between the two variables,  you have decided that you must swap the explanatory and response variables. After refitting the regression model to the data, you expect that:

Correct option is D

Correct Option: D: The value of SSE (sum of squared errors) will change.

Explanation:
In simple linear regression, swapping the explanatory (X) and response (Y) variables changes the regression line because the line is fit to minimize the sum of squared errors (SSE) in the direction of the chosen response variable. This change affects the slope, intercept, and SSE, but not the correlation coefficient (r) or the coefficient of determination (R²), which are symmetric measures.

Information Booster:
1. Swapping X and Y changes which variable’s errors are minimized, so the SSE will generally differ.
2. The new regression line is not simply the inverse of the original; it minimizes vertical errors relative to the new Y.
3. The Pearson correlation coefficient r remains unchanged because it is symmetric: r_XY = r_YX .
4. R²also remains the same since R² = r².
5. The slope does change, but the sign may or may not change depending on the correlation direction.

Additional Knowledge:
* Option (A) The value of correlation will change → Incorrect: Correlation is symmetric and does not depend on which variable is explanatory.
* Option (B) The sign of slope will change → Not necessarily: The sign of the slope is determined by the sign of the correlation, which stays the same. The magnitude changes, but the sign remains unchanged if the relationship direction is the same.
*Option (C) The value of coefficient of determination will change → Incorrect: R² is the square of the correlation coefficient, so it remains the same after swapping variables.