I think I’ve found an inconsistency in the solution of this topic regarding the Durbin Watson test. In the vignette is stated:
“Charlent recalls that the null hypothesis of no positive serial correlation is rejected if the calculated Durbin–Watson (DW) statistic is less than the lower critical value and that the null hypothesis of no negative serial correlation is rejected if the calculated DW statistic exceeds 4 minus the lower critical value.”
In the solution:
“The value of the DW statistic exceeds the upper critical value (1.9566 > 1.73). We fail to reject the null hypothesis of no positive serial correlation. The value of the DW statistic is less than the value (4 – 1.59) = 2.41. Thus, we also fail to reject the null hypothesis regarding negative serial correlation.”
To me the last sentence is wrong and it should be: Thus, we also fail to reject the null hypothesis regarding NO negative serial correlation.
“also fail to reject the null hypothesis regarding negative serial correlation.”
I don’t think they mean that we fail to reject negative serial correlation. It’s more like regarding the topic of negative serial correlation, we should reject the null hypothesis, which is that they are no negative serial correlation.
the part in bold is what they did not say, but should have read between the lines, but agree with you, badly phrased
Null hypothesis: NO negative serial correlation. Fail to reject --> No negative serial correlation.
To be consistent with the first phrase " We fail to reject the null hypothesis of no positive serial correlation" they should also say "we also fail to reject the null hypothesis regarding NO negative serial correlation.” Just to be really clear and avoid missunderstandings.
I understand what you mean, not reading it for 24 hours was helpful, but in the end, yes really bad phrased!