In a linear graph, there are some columns where an interaction should be assigned to.

For example, in L_8(2^7) the column number 3 is for evaluating an interaction between a factor assigned to the

1st column and another factor assigned to the 2nd column.

Please explain why those specific columns are for evaluating an interaction between the factors assigned

to the 1st and 2nd columns.

Figure 9-15 L. (29 Linear Graphs , Figure 8-5 L8 (27)Degrees of freedom 1 2 3 4 5 6 No. 7 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 3 1 N 2 1 2 2 2 4 1 2 2 2 1 1 1 5 1 1 2 1 1 1 2 1 6 2 1 2 2 2 2 7 2 2 1 1 2 2 1 8 2 2. 1 1 2 1 1 2 +1 +1 +1 +1 +1 +1 +1 =7 Figure 9-15 L. (29 Linear Graphs , Figure 8-5 L8 (27)Degrees of freedom 1 2 3 4 5 6 No. 7 1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 3 1 N 2 1 2 2 2 4 1 2 2 2 1 1 1 5 1 1 2 1 1 1 2 1 6 2 1 2 2 2 2 7 2 2 1 1 2 2 1 8 2 2. 1 1 2 1 1 2 +1 +1 +1 +1 +1 +1 +1 =7