What if a model is gets a non significant in F statistic regressor test but lack of fit test shows that there is no strong evidence of lack of fit What does it mean when  a model is gets a non significant in F statistic regressor test but lack of fit test shows that there is no strong evidence of lack of fit.
Can i still use the linear model if this happens?
 A: Everything is telling you that this model does not fit the data well:

*

*the t-test for the xi estimate gives a p-value that is comfortably above 0.1


*since there is only one variable, the omnibus F test gives the same p-value


*compared the the intercept, the estimate for xi is tiny. Even if this was "significant" I would put it to you that it is likely that this is meaningless in the context of your experiment/study.


*$R^2$ is quite small: 0.18
It is not clear what you want to use this model for, but I would suggest that it is not very useful for anything. I assume you have plotted the data ? Unless there is a clear nonlinear association between the 2 variables, then you will likely need to include some other explanatory variables to obtain a useful model.
A: The insignificance of the lack of fit test is telling you that there is no obvious violation of the linearity assumption.  However, this does not imply that the model is "good" in the sense of prediction: A flat line is still a line, but it is not helpful for prediction.
