Large Prob > F in regression On performing regression in stata, the Prob > F value I obtained is 0.1921. I understand that regression coefficients are not significant at 0.01,0.05 or 0.1% levels. Does this mean that my model is not useful?
Also, the corresponding Prob > t for the three coefficients and intercept are respectively 0.09, 0.93, 0.3 and 0.000.
Doesn't this mean that the first coefficient is significant at 0.1% level? What about the intercept term?
 A: The F-test for a regression model tests whether the slopes (not the intercept) are jointly different from 0. The null hypothesis is false when any of the slopes are different from 0. A large p-value for the F-test means your data are not inconsistent with the null hypothesis, and there is no evidence that any of your predictors have a linear relationship with or explain variance in your outcome. "Redundant" is not the word I'd use to describe your model; it's just not very useful or informative.
Your second question seems to amount to how the p-value on the F-statistic could ever be higher than the highest p-value for the t-tests on the slopes. That's an interesting question that I hope someone else could weigh in on. My intuitions are that type I error rate on the slope t-tests is actually higher than nominal because of the multiple comparisons. That is, with many slopes, there's a good a chance one of them will be significant even if they were all 0 in the population. On the other hand, the F-test is a single joint test that doesn't suffer from familywise inflation of the type I error rate. 
Typically, if the F-test is nonsignificant, you should not interpret the t-tests of the slopes. You have already failed to find evidence that any of the slopes are different from 0.
A: In the output for a regression model with $m$ explanatory variables, the value Prob > F-value is the p-value for the goodness-of-fit test, which tests the hypothesis that none of those variables have a relationship with the response variable.  This test uses the hypotheses:
$$H_0: \beta_1 = \cdots = \beta_m = 0 \quad \quad \quad H_A: H_0 \text{ not true}.$$
Your p-value of 0.1921 means that there is no statistically significant evidence to reject the null hypothesis.  Thus, there is no evidence of a relationship (of the kind posited in your model) between the set of explanatory variables and your response variable.
