What affects the accuracy of a prediction?

The predicted response at X is

  =  b0 + b1 x

and has a normal distribution with mean

μy  =  β0  +  β1x

Its standard deviation depends on the value x at which the prediction is being made. The further x is from its mean in the training data, , the greater the variability in the prediction.

Simulation

The effect of the x-value on the variability of the predicted response can be shown using least squares lines fitted to simulated data:

The diagram below shows two theoretical distributions from the above model. (The spread would be even greater for predicting at x = 10.)