r2 vs. fstat and tstat tests

#1
When looking at r2, fstat and tstat and p-value.

To see if the independent variable is a good predictor of the dependent variable...

if you see you have a r2 of 48% but the tstat>t critical and pvalue > .05, and fstat > fritical you reject Ho, and say there is a significant relationship between the 2 variables.

Can you say the independent variable is a good predictor of the dependent variable even if r2% is low?
 

trinker

ggplot2orBust
#2
The [TEX]{R}^2 [/TEX]stat is the amount of variance in the dependent variable explained by your model. The F stat is whether your model is significant. [TEX]{R}^2[/TEX] is a moot point if the model isn't significant. The t stats (if it's a linear model of more than one predictor) is a measure of whether or not the individual predictors are significant predictors of the dependent variable. The rejection of HO depends on what HO is. If it's about your overall model(s) you may look at the F and/or [TEX]{R}^2 [/TEX]. If you're HO is about the predictors you look at the t stat (but only if your overall model is significant).

So to answer your question if F critical is sig and one of the tstats is sig and even though [TEX]{R}^2 [/TEX] is low you may say that the predictor is a significant predictor of the DV. You'll want an effect size to back this up, usually a standardized beta or [TEX]{r}^2 [/TEX] (simple correlation squared). I would avoid saying that something is a good predictor and stick to more conservative APA friendly talk.