The correct answer is: B. the coefficient of determination would be 0.
The coefficient of determination is a measure of how well the data fits the regression line. It is calculated by taking the square of the correlation coefficient. If the correlation coefficient is 0, then the coefficient of determination will also be 0. This means that there is no linear relationship between the variables and the regression line does not fit the data at all.
The correlation coefficient is a measure of the strength of the linear relationship between two variables. It is calculated by taking the covariance of the variables and dividing it by the product of their standard deviations. If the correlation coefficient is 0, then there is no linear relationship between the variables.
The sse is the sum of the squared errors of the regression line. It is calculated by taking the squared difference between the actual values of the dependent variable and the values predicted by the regression line. If the correlation coefficient is 0, then the sse will be equal to the total sum of squares of the dependent variable. This means that the regression line does not predict any of the variation in the dependent variable.
In conclusion, if X and Y in a regression model are totally unrelated, the coefficient of determination would be 0.