The linear bias is the average of all the differences between forecast and observation over the verification sample.
It is calculated either by averaging observation differences or by subtracting the mean observation from the forecast.
Normally the bias is expressed as (forecast-observation) which means that the positive values indicate that the
forecast is too high on average ("overforecasting") and negative values indicate that the forecast is too low
on average ("underforecasting"). The full term "linear bias" is used to avoid confusion with the frequency bias,
which is a score used in verification of forecasts of categorical variables.
The bias indicates whether the average deviation of the forecast from the observations is positive or negative,
but doesn’t give any indication of the magnitude of the errors. It is possible for the bias to be 0 (perfect=no bias),
but all the forecasts could actually have quite large errors. The bias has a range of -∞ to +∞.
Loading Questions
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Suppose on two consecutive days you forecast maximum temperatures of 10 and 9.
The observations were 8 and 12. The model forecast 11 and 8 for the same 2 days. Which of the following
statements are true regarding these forecasts?
Correct. The errors were +2 and -3 degrees for a mean error of -0.5 degrees,
a slight negative bias.
Correct. My forecast error is smaller than the model’s in an absolute sense on both days.
But this fact may not be indicated in the bias because errors of opposite sign can cancel out.
Correct. The bias error is equal.
