# Find the orthogonal contrasts of the sources of variations in the following design

I know the condition of what an orthogonal contrast is: the dot product of their coefficients should be zero. Plus if we are given a set of contrasts, they are supposed to be mutually orthogonal to one another.

This is the solution to the question but I can't seem to understand why:

All I have as an explanation is this:

I can see that the degrees of freedom add up to 5 which is one less than 6, the number of variables. But I still don't get how we derived the expressions.

I can see that those expressions satisfy those conditions. But I can't understand how we derived it.

1) The sum of the coefficients in each linear contrast must sum to zero, and

2) The sum of the products of the corresponding coefficients in any two contrasts must equal zero

• I've asked the question and no one has replied for days. – Anshuman Kumar Dec 22 '19 at 8:38
• If you type out the relevant parts of the post instead of using pictures, maybe then it will generate better response. – StubbornAtom Dec 22 '19 at 8:42
• stats.stackexchange.com/questions/441558/… – StubbornAtom Dec 23 '19 at 11:56