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, such that 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 parameter. Phi is only meaningful for Binomial (1/batch or trial size) and for Gaussian (variance).
Distribution 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).
Link Description 1 Identity (residuals ~ Normal distribution) 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, returns the lower limit.
upper description 0 return lower limit 1 return upper limit

## Remarks

- The underlying model is described here.
- GLM_FORECI returns an array of size equal to number of rows in the input response (Y) or explanatory variables (X).
- The number of rows in response variable (Y) must be equal to number of rows of the explanatory variables (X).
- The betas input is optional, but if the user provide one, the number of betas must equal to the number of explanatory variables (i.e. X) plus one (intercept).
- For GLM with Poisson distribution,
- The values of response variable must be non-negative integers.
- The value of the dispersion factor (Phi) must be either missing or equal to one.

- For GLM with Binomial distribution,
- The values of the response variable must be 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).

- For GLM with Gaussian distribution, the dispersion factor (Phi) value must be positive.

## Files Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

## Comments

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