# GLM_FORECI - GLM Forecasting Confidence Interval

Calculates the standard deviation (sigma of the error terms (epsilon)) of the GLM model, given the values of explanatory variables.

## Syntax

GLM_FORECI (X, Betas, Phi, Lvk, Alpha, Upper)

X
is the independent variables data matrix, so each column represents one variable.
Betas
are the coefficients of the explanatory variables (a one-dimensional array of cells (e.g., rows or columns)).
Phi
is the GLM dispersion paramter. Phi is only meaningful for Binomial (1/batch or trial size) and Gaussian (variance).
Value Phi
Gaussian Variance.
Poisson 1.0.
Binomial Reciprocal of the batch/trial size).
Lvk
is the link function that describes how the mean depends on the linear predictor (1 = Identity (default), 2 = Log, 3 = Logit, 4 = Probit, 5 = Log-Log).
Value Lvk
1 Identity (Residuals ~ Normal distribution) (default).
2 Log (Residuals ~ Poisson distribution).
3 Logit (Residuals ~ Binomial distribution).
4 Probit (Residuals ~ Binomial distribution).
5 Complementary log-log (Residuals ~ Binomial distribution).
Alpha
is the statistical significance level. If missing, a default of 5% is assumed.
Upper
If true, returns the upper confidence interval limit. Otherwise, it returns the lower limit.
Value Upper
0 Returns the lower limit.
1 Returns the upper limit.

## Remarks

1. The underlying model is described here.
2. GLM_FORECI returns an array of size equal to the number of rows in the input response (Y) or explanatory variables (X).
3. The number of rows in the response variable (Y) must equal the number of rows of the explanatory variables (X).
4. The betas input is optional, but if the user provides one, the number of betas must equal the number of explanatory variables (i.e., X) plus one (intercept).
5. For GLM with Poisson distribution,
• The values of the response variable must be non-negative integers.
• The value of the dispersion factor (Phi) must be either missing or equal to one.
6. For GLM with Binomial distribution,
• The values of the response variable must be a non-negative fraction between zero and one, inclusive.
• The value of the dispersion factor (Phi) must be a positive fraction (greater than zero and less than one).
7. For GLM with Gaussian distribution, the dispersion factor (Phi) value must be positive.