Imagine a regression with 3 predictors and one dependent variable with a sample size over 400. Only one predictor has a positive significant effect, p value equals to .02 aprox. R-squared is low (less than .03) and the R-squared IC 95% includes negative values: I have read that this means my model has worse fit than a horizontal line. Therefore, how to interpret this result? If my model is poor, how can I explain the significant effect of one predictor?
To check for the significance of predictors, i.e. if at least one of your predictors is useful to predict the response, you should look at the F-statistic. In a multiple regression case, you should test whether all your coefficients are zero.
$ H_o: \beta_1 = \beta_2 = ... = \beta_p = 0$
$H_a:$ at least one beta is non-zero.
You can test this with the F-statistic because it adjusts for the number of possible predictors we have. This is not the case if you look at the individual p values. In the latter case, it is possible that one predictor has a p-value below 0.05 by chance, especially if the number of predictors is large. This is because, loosely speaking, by definition around 5 out of 100 predictors will have a p-value below 0.05.