# Curve Estimation Models

You can choose one or more curve estimation regression models. To determine which model to use, plot your data. If your variables appear to be related linearly, use a simple linear regression model. When your variables are not linearly related, try transforming your data. When a transformation does not help, you may need a more complicated model. View a scatterplot of your data; if the plot resembles a mathematical function you recognize, fit your data to that type of model. For example, if your data resemble an exponential function, use an exponential model.

Linear. Model whose equation is Y = b0 + (b1 * t). The series values are modeled as a linear function of time.

Logarithmic. Model whose equation is Y = b0 + (b1 * ln(t)).

Inverse. Model whose equation is Y = b0 + (b1 / t).

Quadratic. Model whose equation is Y = b0 + (b1 * t) + (b2 * t**2). The quadratic model can be used to model a series that "takes off" or a series that dampens.

Cubic. Model that is defined by the equation Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3).

Power. Model whose equation is Y = b0 * (t**b1) or ln(Y) = ln(b0) + (b1 * ln(t)).

Compound. Model whose equation is Y = b0 * (b1**t) or ln(Y) = ln(b0) + (ln(b1) * t).

S-curve. Model whose equation is Y = e**(b0 + (b1/t)) or ln(Y) = b0 + (b1/t).

Logistic. Model whose equation is Y = 1 / (1/u + (b0 * (b1**t))) or ln(1/y-1/u) = ln (b0) + (ln(b1) * t) where u is the upper boundary value. After selecting Logistic, specify the upper boundary value to use in the regression equation. The value must be a positive number that is greater than the largest dependent variable value.

Growth. Model whose equation is Y = e**(b0 + (b1 * t)) or ln(Y) = b0 + (b1 * t).

Exponential. Model whose equation is Y = b0 * (e**(b1 * t)) or ln(Y) = ln(b0) + (b1 * t).