I think the signficance of the ANOVA F-test that precedes your regression results tells you if any of the variables in your model are statistically significant. If your F-test is not significant than you should not observe any significant Betas for the independent variables or intercept in your regression (if you do then you probably have a model fit problem that needs to be addressed).
As to whether or not you should report the results this is a much bigger conceptual issue regarding whether or not non-significant results are still important. I would say yes.
I would clarify that ANOVA is not performed separately, Regression Analysis is performed via SPSS v.17 and Model Summary, ANOVA, and Coefficients tables are being generated by SPSS.
Model Summary table:
R value is 0.13 (showing weak correlation between two predictors)
Adjusted R square value is 0.01 (showing not meaningful variance in dependent variable)
ANOVA table: Sig. is 0.067 which is > 0.05 (showing insignificant p value)
Coefficients table: between two predictors, one predictor is insignificat (sig. value is 0.58)
In above situation, I would like to be advised if i should report regression model and equation in my report just like if ANOVA would've been significant or i should not report because of ANOVA which is insignificant.
I understood from above response that it depends on situation. Please advise if there is any rule of thumb kind thing or any condition to report regression model which depends on ANOVA significance.