Which of the following conditions must be fulfilled for the Durbin–Watson test to be valid? (i) The regression includes a constant term(ii) The regressors are non-stochastic(iii) There are no lags of the dependent variable in the regression(iv) There are no lags of the independent variables in the regressionGroup of answer choices(i), (ii), and (iv) only(i), (ii), (iii), and (iv)(i), (ii), and (iii) only(i) and (ii) only

The Durbin-Watson test is used to detect the presence of autocorrelation (a relationship between values separated from each other by a given time lag) in the residuals (prediction errors) from a regression analysis. For the Durbin-Watson test to be valid, the following conditions must be fulfilled:

(i) The regression includes a constant term: This is necessary because the test is based on the assumption that the errors (residuals) from the regression have a mean of zero. If the regression does not include a constant term, this assumption may not hold.

(ii) The regressors are non-stochastic: This means that the independent variables (regressors) are not random variables. If they are random, the test may not be valid.

(iii) There are no lags of the dependent variable in the regression: The Durbin-Watson test is not applicable to models where the dependent variable is lagged. If there are lags of the dependent variable, other tests for autocorrelation should be used.

(iv) There are no lags of the independent variables in the regression: Similar to (iii), the Durbin-Watson test is not applicable to models where the independent variables are lagged.

So, the correct group of answer choices is (i), (ii), (iii), and (iv).