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 C

The correct answer is: (c) The value of coefficient of determination will change

Explanation:
When you swap the explanatory and response variables in a regression analysis, the following changes occur:

• Correlation: The value of correlation remains the same. Correlation measures the strength and direction of a linear relationship between two variables, and it is symmetric. Therefore, swapping the variables does not change the correlation value.

• Slope: The sign of the slope will not necessarily change. The slope in a linear regression model is determined by the relationship between the dependent and independent variables, but swapping the explanatory and response variables does not inherently change the sign of the slope.

• Coefficient of determination (R²): The coefficient of determination (R²) will remain the same. R² measures the proportion of variance explained by the model. When you swap the variables, the proportion of variance explained does not change, although the explanatory variable has changed.

• SSE (sum of squared errors): SSE represents the sum of the squared differences between the observed and predicted values. Changing the variables may affect the predicted values, leading to a change in SSE. Swapping the variables often results in a different set of predicted values, which affects the SSE.