On interpreting the statistical significance of R squared

I have performed a linear regression analysis to two series of data, each of which has 50 values. I did the analysis in SPSS and as a result got a table which says that my adjusted R squared is 0.145 and its significance is 0.004.

Being 0.004 < 0.05, I assume my adjusted R squared is significant.

1) Does it mean my adjusted R squared is credible?

2) What does happen if you get a significance which is > 0.05? Does it imply the adjusted R squared can be trusted with credibility but also that the two datasets are not or poorly correlated?

EDIT

I think I can condense my last question into: does a statistically non-significant R squared nullify the validity of the calculated R squared?

• What distinctions, exactly, are you making between "credible," "correlated," and "significant"? Although the latter two terms have commonly understood meanings, the first one is ambiguous. – whuber Nov 11 '15 at 19:56
• Well, it sounds ambiguous to me that there is a procedure which computes R and then tells you if it is statistically significant. In this context I think I can maintain credible means acceptable or trustworthy. – FaCoffee Nov 11 '15 at 19:57
• I think I can condense my last question into: does a statistically non-significant R squared nullify the validity of the calculated R squared? – FaCoffee Nov 11 '15 at 20:00
• I suspect many of your uncertainties about the meaning of this output may be addressed at stats.stackexchange.com/questions/31 : please take a look. – whuber Nov 11 '15 at 20:06