Editing Analysis of covariance (section)

==Assumptions==
There are several key assumptions that underlie the use of ANCOVA and affect interpretation of the results.<ref name="Montgomery, Douglas C 2012"/> The standard [[regression analysis|linear regression]] assumptions hold; further we assume that the slope of the covariate is equal across all treatment groups (homogeneity of regression slopes).

===Assumption 1: linearity of regression ===
The regression relationship between the dependent variable and concomitant variables must be linear.

===Assumption 2: homogeneity of error variances===
The error is a random variable with conditional zero mean and equal variances for different treatment classes and observations.

===Assumption 3: independence of error terms===
The errors are uncorrelated. That is, the error covariance matrix is diagonal.
[[File:Homogeneity of Regression Slopes.png|thumb|308x308px]]

===Assumption 4: normality of error terms===
The [[Errors and residuals in statistics|residuals (error terms)]] should be normally distributed <math>\epsilon_{ij}</math> ~ <math>N(0, \sigma^2)</math>.

===Assumption 5: homogeneity of regression slopes===
The slopes of the different regression lines should be equivalent, i.e., regression lines should be parallel among groups.

The fifth issue, concerning the homogeneity of different treatment regression slopes is particularly important in evaluating the appropriateness of ANCOVA model. Also note that we only need the error terms to be normally distributed. In fact both the independent variable and the concomitant variables will not be normally distributed in most cases.