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?
On interpreting the statistical significance of R squared
statistics;correlation
The p-value is the strength of evidence against the null hypotheses. In this case the null is that the coefficient is equal to zero. So your p-value says that this is very weak evidence against the null so you model is likely to be describing the underlying system of the data.R-squared describes the percent of variation that is explained by the model. Your value is very low; 14.5%. Of all the activity in the data your model is only explaining 14.5% of it.So you have a situation were model is most likely explaining variation in data but not explaining very much of it.  I would suggest altering the model and refitting. 