What is the residual standard deviation?
Can I see whether the model I used is accurate or not by looking at this measure?
In fact, I try to understand whether my data set is fitting to linear model or non-linear model. If fitting non-linear data set to linear model, what is the result? how to understand (which regression results?) model mistakes?
Thank you for helping.
1) By looking at the Mean Squared Error (MSE), $MSE = \frac{1}{n-p}\sum_{i=1}^n(\hat{y}_i - y_i)^2 $, or its square root, you can get some indication regarding the goodness of fir of your model. As in a common regression model, one of the main indicators for this measure is $R^2$, which defined as $$ R^2 = \frac{\sum_{i=1}^n(\hat{y}_i- \bar{y}_i)^2 }{\sum_{i=1}^n(y_i - \bar{y})^2} = 1 - \frac{\sum_{i=1}^n(\hat{y}_i- y_i)^2 }{\sum_{i=1}^n(y_i - \bar{y})^2}. $$ Due to the fact the $SST = \sum(y_i - \bar{y})^2$ is independent of a fitted model, the residuals sum of squared, $SS{res} = \sum(\hat{y}_i - y_i)^2$, determines the $R^2$.
2) I'm not sure what means the term "non linear data". Basically, if you want to select among different possible models you can use some criteria like AIC and BIC. If you want to check the goodness of fit of a given model, $R^2$, generilzed $R^2$ and the $LR$ value may help you. So, as your question is pretty general, I'll try to give you some links for further reading.
a) Deviance (the equivalent of the $SSres$ for generalized linear models).
b) Model Selection in the statistical framework.
c) AIC and its generalized version.