Attachments



To determine the difference between the extrapolation and interpolation, we must look at the prefix "extra" and "Inter".The prefix "extra" literally means - "outside" or "addition".The prefix "inter" means - "between" or "protection".Knowing this, you can easily distinguish between the methods themselves.

Use of



Both methods assume some initial conditions.First, you must determine what will be independent, and that the dependent variable in our case.With the help of data collection is a series of double values.It is also necessary to formulate a model for the original data.All this can be written in the table for the best clarity.Then plotted.They are often an arbitrary curve, which a
pproximately describes the data.In any case, there is a function that links the independent variable to the dependent.

purpose of these transformations is not only the model itself.Typically, it is used for prediction.In particular, it should be considered an independent variable that is the predicted value of the dependent variable corresponding to it.The output value of the independent variable will indicate whether extrapolation was used or interpolation.

Interpolation



You can use the resulting function to predict the value of the dependent variable to the independent, which is implicitly expressed.In this case, the method of interpolation.

Assume that the value of x between 0 and 10 is used to create features:

2x + y = 5;

We can use this function to the best estimate of the value at the corresponding value of x = 6.Simply substitute the value into the original equation.It is easy to see the result:

y = 2 (6) 5 = 17;


Extrapolation



original function can be used to predict the value of the dependent variable for the independent variable, which is out of range.In this case extrapolation.

Suppose, as before the value of x is between 0 and 10 and has a function:

y = 2x + 5;

To assess the value of y using x = 20, it is necessary to substitute this value into our equation:

y = 2 (20) 5 = 45;

If the value of x is not included in the acceptable range, the validation method is called extrapolation.

Note



of the two methods is preferred interpolation.This is so because when it is used there is a great probability of getting a reliable appraisal.When we use the extrapolation, it is assumed that the trend will continue for our values ​​of x outside the range that was originally set.It may not always be so, and therefore need to be very careful when using the method of extrapolation.