User Guide

Chapter
27
Curve Estima
tion
The Curve Estimation procedure produces curve estimation regression statistics and
related plo
ts for 11 different curve estimation regression models. A separate model is
produced for each dependent variable. You can also save predicted values, residuals,
and prediction intervals as new variables.
Example. A
n internet service provider tracks the percentage of virus-infected e-mail
traffic on its networks over time. A scatterplot reveals that the relationship is
nonlinear. You might fit a quadratic or cubic model to the data and check the validity
of assump
tions and the goodness of fit of the model.
Statistics. For each model: regression coefficients, multiple R, R
2
, adjusted R
2
,
standard error of the estimate, analysis-of-variance table, predicted values, residuals,
and predi
ction intervals. Models: linear, logarithmic, inverse, quadratic, cubic, power,
compound, S-curve, logistic, growth, and exponential.
Data. The dependent and independent variables should be quantitative. If you select
Time inst
ead of a variable from the working data file as the independent variable,
the Curve Estimation procedure generates a time variable where the length of time
between cases is uniform. If
Time is selected, the dependent variable should be
a time-s
eries measure. Time-series analysis requires a data file structure in which
each case (row) represents a set of observations at a different time and the length of
time between cases is uniform.
Assump
tions.
Screen your data graphically to determine how the independent and
dependent variables are related (linearly, exponentially, etc.). The residuals of
a good model should be randomly distributed and normal. If a linear model is
used, t
he following assumptions should be met. For each value of the independent
variable, the distribution of the dependent variable must be normal. The variance
of the distribution of the dependent variable should be constant for all values of
the in
dependent variable. The relationship between the dependent variable and the
independent variable should be linear, and all observations should be independent.
425