If residual error is 51 and predicted cost value is 37, then observed cost value will be

The correct answer is $\boxed{\text{A. }14}$.

The residual error is the difference between the observed value and the predicted value. In this case, the observed value is unknown, but we can calculate it by adding the residual error to the predicted value. Therefore, the observed cost value is $14 = 37 + 51$.

Option B is incorrect because the observed cost value cannot be greater than the predicted cost value.

Option C is incorrect because the observed cost value cannot be less than the residual error.

Option D is incorrect because the observed cost value cannot be equal to the residual error.