Select the method or formula of your choice.
GLM model
In matrix terms, this is the formula for the general linear regression model:
Notation
| Term | Description |
|---|---|
| Y | vector of responses |
| X | design matrix |
| β | vector of parameters |
| ε | vector of independent normal random variables |
Fitted value and SE fit for fixed batch
The fitted value is the predicted y or 
, which is the mean response value for the given predictor values using the estimated regression equation.
The standard error of the fitted value in a regression model with one predictor is:
The standard error of the fitted value in a regression model with more than one predictor is:
Notation
| Term | Description |
|---|---|
| xi | ith predictor value |
 | mean predictor |
| X | design matrix |
| n | number of observations |
| s2 | mean square error |
Prediction interval
The range in which the predicted response for a new observation is expected to fall. The formula is:
Notation
| Term | Description |
|---|---|
 | fitted response value for a given set of predictor value |
| α | level of significance |
| n | number of observations |
| p | number of terms in the model, including the intercept term if it is in the model |
| s2 | mean square error |
| x | predictor matrix |
| xo | matrix of given predictor values beginning with a column of 1s when the intercept term is in the model |
Confidence interval
The range in which the estimated mean response for a given set of predictor values is expected to fall. The formula is:
Notation
| Term | Description |
|---|---|
 | fitted response value for a given set of predictor values |
| α | level of significance |
| n | number of observations |
| p | number of terms in the model, including the intercept term if it is in the model |
| s2(b) | variance-covariance matrix of coefficient |
| s2 | mean square error |
| X | predictor matrix |
| Xo | matrix of given predictor values beginning with a column of 1s when the intercept term is in the model |
