Syntax

C#
[SerializableAttribute] public class ANCOVA

Visual Basic (Declaration)
<SerializableAttribute> _ Public Class ANCOVA

Visual C++
[SerializableAttribute] public ref class ANCOVA

Remarks

Class ANCOVA performs analyses for models that combine the features of a one-way analysis of variance model with that of a multiple linear regression model. The basic one-way analysis of covariance model is

$y_{ij}=\beta_{0i}+\beta_{1}x_{ij1}+\beta_{2} x_{ij2}+\ldots+\beta_mx_{ijm}+\varepsilon_{ij}$

$i=1,2,\ldots,ngroup$

$j=1,2,\ldots,n_i$

where, ngroup is the number of treatment groups, the observed value of $y_{ij}$ constitutes the j-th response in the i-th group, $\beta_{0i}$ denotes the y intercept for the regression function for the i-th group, $\beta_{1}$ , $\beta_{2}$ , ..., $\beta_{m}$ are the regression coefficients for the covariates, and the $\varepsilon_{ij}$ 's are independently distributed normal errors with mean zero and variance $\sigma^2$ . This model allows the regression function for each group to have different intercepts. However, the remaining m regression coefficients are the same for each group, i.e., the regression functions are parallel.

In practice, sometimes the regression functions are not parallel. In addition to estimates for the model assuming parallelism (parallel regression planes), ANCOVA computes estimates and summary statistics for the separate regressions of each group. These estimates can be examined using the methods GetCoefficientTables and GetANOVATables.

Estimates for the $\beta_{0i}$ 's and $\beta_{1}$ , $\beta_{2}$ , ..., $\beta_{m}$ in the model assuming parallelism are returned using the method GetModelCoefficients. Summary statistics are also computed for this model and returned by the Compute method.

The adjusted group means, stored in the last column of xymean, are computed using the formula:

$\hat{\beta}_{0i}+\hat{\beta}_{1} \overline{x}_{1}+\hat{\beta}_{2}\overline{x}_{2}+\ldots+ \hat{\beta}_{m}\overline{x}_{m}$

where xymean is the matrix returned by GetMeans and ncov is the number of covariates.

The estimated covariance between the $i_{1}$ -th and $i_{2}$ -th adjusted group mean is given by

$\nu_{i_{1}i_{2}}+\sum_{r=1}^{m}\sum_{s=1}^{m} \overline{x}_{r}\nu_{k+r, k+s}\overline{x}_{s}+\sum_{r=1}^{m} \overline{x}_{r}\nu_{i_{1}, k+r}+\sum_{r=1}^{m}\overline{x}_{r} \nu_{i_{2}, k+r}$

where $\nu_{pq}$ is the entry in covb[p-1][q-1], where covb is returned by GetVarCovCoefficients and is the estimated covariance between the p-th and q-th estimated coefficients in the regression function.

Inheritance Hierarchy

System..::.Object
Imsl.Stat..::.ANCOVA

Syntax

Remarks

Inheritance Hierarchy

See Also