How can I check model assumptions when all my residuals are zero?

#1
I'm doing a 2^4 full factorial experiment. I have 1 continuous response Y and 4 factors, each with 2 levels, yielding a total of 16 level combinations. The experiment is unreplicated and I have a total 16 observations, one for each level combination.

The design matrix has only 1's and -1's, and the columns are orthogonal.

The residuals of this model are all 0. In this case how can I check that the regression assumptions such as constant variance and normality of residuals hold?
 
#2
That is because you have the full model. You are estimating 16 parameter. One parameter for each obervation. That is the same as estimating 16 means, each one from one observation.

You have 1 intecept+ 4 main effects + 6 two_factor_interactions + 4 three_factor_interactions + 1 four_factor_interaction =16
# 1 + 4 main + 6(2fi) + 4(3fi) + 1(4fi)= 16

Take away the four_factor_interaction and you will get residuals that are not zero.

One common procedure is to take away non-significant higher interactions.

Do a QQ-plot for the estimated parameters. If they are all on a streight line then they are all random numbers. If they deviate from a streight line then the factor is "significant".