# What is the covariance matrix in regression?

## What is the covariance matrix in regression?

In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector.

How do you create a covariance matrix in SAS?

To form the covariance matrix for these data:

1. Use the horizontal concatenation operator to concatenate the vectors into a matrix whose columns are the vectors.
2. Center each vector by subtracting the sample mean.
3. Form the CSSCP matrix (also called the “X-prime-X matrix”) by multiplying the matrix transpose and the matrix.

What is the SPEC test in SAS?

The SPEC option tests a joint null hypothesis of the following: the errors are homoscedastic. the errors are independent of the regressors. the model is correctly specified.

### What is Vif in SAS?

vif stands for variance inflation factor. As a rule of thumb, a variable whose VIF values is greater than 10 may merit further investigation. Tolerance, defined as 1/VIF, is used by many researchers to check on the degree of collinearity. A tolerance value lower than 0.1 is comparable to a VIF of 10.

How do you calculate VIF in SAS?

The VIF option in the regression procedure can be interpreted in the following ways:

1. Mathematically speaking: VIF = 1/(1-R-square)
2. Procedurally speaking: The SAS system put each independent variables as the dependent variable e.g.
3. Graphically speaking: In a Venn Diagram, VIF is shown by many overlapping circles.

Why covariance matrix is important?

The covariance matrix provides a useful tool for separating the structured relationships in a matrix of random variables. This can be used to decorrelate variables or applied as a transform to other variables. It is a key element used in the Principal Component Analysis data reduction method, or PCA for short.

## How do I use sample covariance and correlation matrices in SAS?

Sample covariance matrices and correlation matrices are used frequently in multivariate statistics. This post shows how to compute these matrices in SAS and use them in a SAS/IML program. There are two ways to compute these matrices: Compute the covariance and correlation with PROC CORR and read the results into PROC IML.

How do I calculate the covariance and correlation matrices?

If the data are in SAS/IML vectors, you can compute the covariance and correlation matrices by using matrix multiplication to form the matrix that contains the corrected sum of squares of cross products (CSSCP).

How do you calculate covariance and correlation in Proc IML?

Computation of the covariance and correlation matrix in PROC IML. If the data are in SAS/IML vectors, you can compute the covariance and correlation matrices by using matrix multiplication to form the matrix that contains the corrected sum of squares of cross products (CSSCP).

### What is analysis of covariance?

Analysis of covariance combines some of the features of both regression and analysis of variance. Typically, a continuous variable (the covariate) is introduced into the model of an analysis-of-variance experiment.