What is a null model in regression and how does it relate to the null hypothesis? What is the null model in regression and what's the relationship between the null model and the null hypothesis?
From my understanding, does it mean

*

*Using "an average of the response variable" to predict the continuous response variable?

*Using the "label distribution" in predicting discrete response variables?

If that is the case, it seems there are missing connections between the null hypothesis.
 A: In regression, as described partially in the other two answers, the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null hypothesis, there is no trend and the best estimate/predictor of a new observation is the mean, which is 0 in the case of no intercept.
A: A null model is related to a null hypothesis. Take the following univariate model:
$Y=\alpha+\beta_{1}X + \epsilon$
My null hypothesis would normally be that $\beta_{1}$ is statistically no different from zero.
$H_{0}: \beta_{1}=0$ (null hypothesis)
$H_{A}: \beta_{1}\neq 0$ (alternative hypothesis)
For a univariate linear model, such as the above, if we were to reject the alternative hypothesis then  we could drop  $\beta_{1}X$ from the linear model and we'd be left with
$Y = \alpha + \epsilon$
Which is your Null model and the same as mean of $Y$.
A: No, I would say "null model" essentially has the same meaning as "null hypothesis":  the model if the null hypothesis is true.   What this means, in a particular case, of course depends upon the concrete null hypothesis.  
Your interpretations as "the average value" (you probably want to say "the marginal distribution on response variable") not taking into account any predictors, is one possibility, corresponding to the null hypothesis of an "omnibus test", testing all the parameters (except the intercept) simultaneously.
But interest could well focus on a model of the form
$$
    y_i = \beta_0 + \beta_1^T x_{1i} + \beta_2^T x_{2i} + \epsilon_i
$$
where $x_1$ contains the predictors you know are affecting the outcome, so are not wanting to test, while $x_2$ contains the predictors you are testing.   
So the null hypothesis will be $\beta_2 =0$ and the null model would be 
$y_i = \beta_0 + \beta_1^T x_{1i}  + \epsilon_i$.  So it depends. 
