# Methods and formulas for event predictions in Binary Fitted Line Plot

Select the method or formula of your choice.

## Fitted and predicted values

Different models have different link functions. To calculate the prediction, invert the link function for the model. The inverse functions are in this table.

Model Link Function Formula for Prediction
Binomial Logit Binomial Normit Binomial Gompit Poisson Natural log Poisson Square root Poisson Identity ### Notation

TermDescription
exp(·) the exponential function
Φ(·) the cumulative distribution function of the normal distribution
X' the transpose of the vector of points to predict for the vector of estimated coefficients

## Standard error of fitted values and predictions

### Notation

TermDescription
Φ1, for the binomial and Poisson models
xhthe vector of a new design point the transpose of xh
Xthe design matrix
Wthe weight matrix the first derivative of the link function evaluated at  the predicted mean response

## Confidence limits for fits and predictions

The confidence limits use the Wald approximation method. This is the formula for a 100(1 − α)% two-sided confidence interval:

### Notation

TermDescription the inverse of the link function evaluated at x   the transpose of the vector of the predictors the vector of estimated coefficients the value of the inverse cumulative distribution function for the normal distribution evaluated at αthe significance level  Xthe design matrix
Wthe weight matrix 1, for binomial and Poisson models
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