What Are Stats Metrics To Analyze How Well One Column Predicts Another Column I have the following table with three columns: 

Type    Category    Actual
A       1           47
A       1           90
A       1           74
A       2           64
A       2           25
A       3           55
A       3           55
A       3           19
B       6           80
B       6           28
B       2           60
B       2           49
B       2           7


Next, I'm given a static table that provides predictions by Type and Category.  I will be using the "Prediction" column values as the actual predictions.  

Type    Category    Prediction
A       1           83
A       2           48
B       6           54
B       2           57


So once I combine the two tables by Type and Category, I have the following table:    

Type    Category    Actual  Prediction
A       1           47      83
A       1           90      83
A       1           74      83
A       2           64      48
A       2           25      48
B       6           80      54
B       6           28      54
B       2           60      57
B       2           49      57
B       2           7       57


I want to evaluate my data by distinct Type and Category combinations.  So my output table could be something like this: 

Type    Category    Avg_Actual  Avg_Prediction
A       1           value       value 
A       2           value       value
B       6           value       value
B       2           value       value 


My question is: What are different metrics I can use to evaluate how predictive the "Prediction" column is against the "Actual" values given my data set.  

Please be specific with your metrics and the more you can provide (with details on how to derive them) the better.  So far, the only one I came up with was calculating RMSE.  

I would like all the metrics at a distinct Type-Category level.  Additionally, is there a way to incorporate confidence intervals into this analysis?  

Any help is greatly appreciated.
Other possible evaluation measures are:


Mean Absolute Error (MAE): $\frac{\sum_{i=1}^n{\| y_i - x_i\|}}{n}$
R^2: also known as coefficient of determination, the formula is rather lengthy, but a detailed definition, as well as a motivation, can be found here
Root Mean Squared Logarithmic Error (RMSLE): $\sqrt[]{\frac{1}{n}\sum_{i=1}^n{(\log(y_i + 1) - \log(x_i + 1))^2}}$
Explained Variance Score: $1 - \frac{Var(y - x)}{Var \ y}$ more here and here.
Mean absolute percentage error (MAPE): see the wikipedia for the formula and major drawbacks of this measure.
Median Absolute Error (MAE2): $Median(| y_1 - x_1 | \dots | y_n - x_n |)$


These measures, as well as others, can be found here together with some Python code.