Available with 3D Analyst license.
Summary
Interpolates a raster surface from points using a trend technique.
Usage
As the order of the polynomial is increased, the surface being fitted becomes progressively more complex. A higherorder polynomial will not always generate the most accurate surface; it is dependent on the data.
The optional RMS file output contains information on the RMS (root mean square) error of the interpolation. This information can be used to determine the best value to use for the polynomial order, by changing the order value until you get the lowest RMS error. See How Trend works for information on the RMS file.
For the LOGISTIC option of Type of regression, the zvalue field of input point features should have codes of zero (0) and one (1).

Some input datasets may have several points with the same x,y coordinates. If the values of the points at the common location are the same, they are considered duplicates and have no effect on the output. If the values are different, they are considered coincident points.
The various interpolation tools may handle this data condition differently. For example, in some cases, the first coincident point encountered is used for the calculation; in other cases, the last point encountered is used. This may cause some locations in the output raster to have different values than what you might expect. The solution is to prepare your data by removing these coincident points. The Collect Events tool in the Spatial Statistics toolbox is useful for identifying any coincident points in your data.
Syntax
Trend_3d (in_point_features, z_field, out_raster, {cell_size}, {order}, {regression_type}, {out_rms_file})
Parameter  Explanation  Data Type 
in_point_features  The input point features containing the zvalues to be interpolated into a surface raster.  Feature Layer 
z_field  The field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input point features contain zvalues. If the regression type is Logistic, the values in the field can only be 0 or 1.  Field 
out_raster  The output interpolated surface raster. It is always a floatingpoint raster.  Raster Layer 
cell_size (Optional)  The cell size at which the output raster will be created. This will be the value in the environment if it is explicitly set; otherwise, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.  Analysis Cell Size 
order (Optional)  The order of the polynomial. This must be an integer between 1 and 12. A value of 1 will fit a flat plane to the points, and a higher value will fit a more complex surface. The default is 1.  Long 
regression_type (Optional)  The type of regression to be performed.
 String 
out_rms_file (Optional)  File name for the output text file that contains information about the RMS error and the ChiSquare of the interpolation. The extension must be .txt.  File 
Code Sample
Trend example 1 (Python window)
This example inputs a point shapefile and interpolates the output surface as a TIFF raster.
import arcpy
from arcpy import env
env.workspace = "C:/data"
arcpy.Trend_3d("ca_ozone_pts.shp", "ozone",
"C:/output/trendout.tif", 2000, 2, "LINEAR")
Trend example 2 (standalone script)
This example inputs a point shapefile and interpolates the output surface as a Grid raster.
# Name: Trend_3d_Ex_02.py
# Description: Interpolate a series of point features onto a
# rectangular raster using a trend technique.
# Requirements: 3D Analyst Extension
# Import system modules
import arcpy
from arcpy import env
# Set environment settings
env.workspace = "C:/data"
# Set local variables
inPointFeatures = "ca_ozone_pts.shp"
zField = "ozone"
outRaster = "C:/sapyexamples/output/trendout02"
cellSize = 2000.0
PolynomialOrder = 2
regressionType = "LINEAR"
# Check out the ArcGIS 3D Analyst extension license
arcpy.CheckOutExtension("3D")
# Execute Trend
arcpy.Trend_3d(inPointFeatures, zField, outRaster, cellSize,
PolynomialOrder, regressionType)
Environments
Licensing Information
 ArcGIS for Desktop Basic: Requires 3D Analyst or Spatial Analyst
 ArcGIS for Desktop Standard: Requires 3D Analyst or Spatial Analyst
 ArcGIS for Desktop Advanced: Requires 3D Analyst or Spatial Analyst