If a trend exists in your data, it is the nonrandom (deterministic) component of a surface that can be represented by a mathematical formula. For instance, a gently sloping hillside can be represented by a plane. A valley would be represented by a more complex formula (a second-order polynomial) that creates a U shape. This formula may produce the representation of the surface you want. However, many times the formula is too smooth to accurately depict the surface because no hillside is a perfect plane nor is a valley a perfect U shape. If the trend surface does not adequately portray the surface well enough for your particular need, you may want to remove it and continue with your analysis, modeling the residuals, which is what remains after the trend is removed. When modeling the residuals, you will be analyzing the short-range variation in the surface. This is the part that isn't captured by the perfect plane or the perfect U shape.

The Trend Analysis tool enables you to identify the presence or absence of trends in the input dataset.

To do so, click the Geostatistical Analyst drop-down arrow, point to Explore Data, then click Trend Analysis. Click the Layer drop-down arrow and click ca_ozone_pts. Click the Attribute drop-down arrow and click OZONE.

Each vertical stick in the trend analysis plot represents the location and value (height) of each data point. The points are projected onto the perpendicular planes, an east–west and a north–south plane. A best-fit line (a polynomial) is drawn through the projected points, which model trends in specific directions. If the line were flat, this would indicate that there would be no trend. However, if you look at the light green line in the image above, you can see it starts out with low values and increases as it moves east until it levels out. This demonstrates that the data seems to exhibit a strong trend in the east–west direction and a weaker one in the north–south direction.

Click the Rotate Projection scroll bar and scroll left until the rotation angle is 30 degrees.

This rotation enables you to see the shape of the east–west trend more clearly. You can see that the projection actually exhibits an upside-down U shape. Because the trend is U shaped, a second-order polynomial is a good choice to use for the global trend. Even though the trend is being exhibited on the east–west projection plane, because the points were rotated 30 degrees, the actual trend is northeast to southwest. This trend is possibly caused by the fact that the pollution is low at the coast, but farther inland there are large human populations that taper off again at the mountains. You will remove these trends in Exercise 4.

Close the Trend Analysis dialog box.