Significance levels of r-squared and adjusted r-squared

[chriss]

Hello everyone,

I am relatively new to the PLS methodology and read alot in this forum.
For most of my questions I have found good advice but the one regarding r² is still worrying me.

My model:
- 2 latent independent variables
- 4 latent dependent variables
- 5 control variables

I hypothesized the direct effect of the two independent variables on the four dependent variables.

When performing a bootstrap procedure (10.000 samples) I was a little worried about the r-squared and adjusted r-squared values.
The results show that one of my r² values for a dependent variables is not significant (p>.05).
The same is true for two of the four adjusted r² values for two dependent variables (p>.05).

What I am struggling with is the interpretation of this:
1. (Out of curiosity:) Is it common or uncommon to have non significant r² and adjusted r² values after bootstrapping?
2. Does this mean that the explained variance of the model ( the r² / adjusted r² values) cannot be taken for granted (because statistically significant)?
3. What is the effect on the path coefficients? Can the significant path coefficient still be interpreted despite non significant r² / adjusted r² for this very dependent variable?
4. What is the effect on the model itself? Is it still useable or should it be dismissed?

I am looking forward to receive your thoughts.
Thanks a lot in advance!

Christian

[Hengkov]

R2 and adjusted R ^ 2 is not interpreted as significant or not, but it was more to explain the variance of the dependent variable.

[chriss]

What is the significance of r² and adjusted r² used for then?
Why would PLS report this after bootstrapping if it is not meant to be interpreted?

[Hengkov]

Both are used to describe various endogenous variable able to be explained by exogenous variables. No, this value is generated from the PLS algorithm, not bootstrapping.