Random Forest, Type - Regression, Calculation of Importance Example
MSE is measure of error of the overall regression model, $\frac{1}{n}\sum\|y_i-\hat y_i\|^2$.

For an important variable, if it is replaced with random noise, you would imagine MSE with the faulty data to increase. IncMSE (Incremental MSE) for a particular variable is how much the MSE will increase if the variable is completely randomized.

This is usually computed on the out-of-bag data.



Node purity is a measure of how homogeneous a node is. An example of node purity is information entropy, i.e. $-p_1\log p_1-p_0\log p_0$ if there are two classes.
For regression models, node impurity is usually taken as the variance in a node.

Everytime you split a node, you do it to make the new nodes homogeneous, hence the purity increases.

IncPurity of a variable is weighted average of incremental purity because of each split by this variable was used to split, with the node population as the weight.