Hi @jpchen, re my comment “multiply the inputs by each weight / distribution”.

sample test data

feature_1, feature_2, feature_3

12, 0, 19

2, 15, 0

**Least squares regression**

In a regular regression problem once the model is trained and to make a prediction on new inputs you would multiply each feature by the corresponding weight and sum the values to output the final prediction for a given sample input.

weights (after training a model): w1=7, w2=18, w3=17

Multiplying the the weights by the the features for each input data sample will output a prediction (without any uncertainty information)

**Probabilistic Linear Regression**

weights (after training a model - linear model so only one set of weights):

w1_mean=7, w1_std=1

w2_mean=18, w2_std=4,

w3_mean=17, w3_std=1

Now that you have the mean value of each weight and standard deviation can you use this information to calculate the uncertainty of a prediction on the test data? i.e w2 has a large standard deviation so any input data with high values for this feature would result in high uncertainty in the prediction.

The second sample test input above has a value of 15 for feature_2 so maybe this would result in high uncertainty in the test prediction.

The first sample has a value of 0 for feature_2 so maybe this would result in a more confident prediction as the other two features effecting the prediction have a low standard deviation?

This is what I mean by using the mean and std of each weight to calculate the uncertainty specific to each new test input.

Does this make sense?