**Select menu: Data | Interpolation**

Interpolation fits a piecewise line or curve through a set of points, then predicts values at intermediate values of x or y using the fitted curve. The values to interpolate must be at points within the range of the given x or y data. If the interpolating curve is Y=F(X), then for a given x, we obtain the interpolated value y = F(x). For inverse interpolation, for a given y, x is found, such that y = F(x), if possible. Two smoothing functions are provided. These do not give a curve that passes through every point, but smooth out random variation around a smooth trend which best fits the data for a given degree of flexibility. This allows predictions to be estimated with reduction in the random variation from point to point.

- After you have imported your data, from the menu select

**Data | Interpolation**.

## Available data

Lists variates that are currently available. Double-click a name to copy it into the edit field or type the name.

## Method

This defines the type of interpolation.

Predict Y from X |
given the x-values, predict the y-values by interpolation. |

Predict X from Y |
given the y-values, predict the x-values by inverse interpolation. |

Predict missing values in both Y and X |
Predict values for the missing observations within both the x and y variates. If a y-value is missing the corresponding x-value is used to interpolate the missing y-value, and vice-versa for missing x-values. |

## Interpolation function

This defines the type of curve fitted to the points in the original series.

Linear |
a straight line joins the points in a piecewise linear function. |

Cubic |
a cubic polynomial is fitted through the 4 points around each interval. |

Cubic smoothing spline |
a cubic smoothing spline with the specified degrees of freedom is fitted to the series using the FIT command. |

REML smoothing spline |
a REML smoothing spline is fitted to the points, where the amount of smoothing is estimated as a variance component. |

## Data to use for interpolation

These two fields define the points in the series being interpolated from.

Y-variate |
variate containing the y-values in the data. |

X-variate |
variate containing the x-values in the data. |

## Interpolated data

Provides fields to specify the values to interpolate at and save the resulting values. These fields are only available when either the **Predict Y from X** or **Predict X from Y** methods are selected. The values to interpolate at can be supplied within a variate, as an individual number or a series of numbers separated by spaces or commas (e.g. 1 3.5 5.8 or 1,3.5,5.8).

Interpolate values at |
contains the known x- or y-values where the y- or x-values will be interpolated at. |

Save interpolated values |
a name of a variate to save the interpolated values. |

## Display in output

When selected, the interpolated values will be displayed in the Output window.

## Display in spreadsheet

When selected, the interpolated values will be displayed in the spreadsheet. If the variate specified in the **Interpolate values at** field is currently open within a spreadsheet, then the values will be added to that spreadsheet, otherwise a new spreadsheet will be created.

## Plot interpolated values

When selected, a graph will be created showing the interpolated points and the data used for interpolation.

## See also

- INTERPOLATE directive
- VINTERPOLATE procedure
- FIT directive
- REML directive
- Calculations menu
- Smoothing spline regression menu
- Linear mixed models (REML) menu
- Data Menu