Consider the multiple regression problem including an intercept with the following list of explanatory variables: for i = 1,... ,N. a) Show that the last six variables (c4, s4, ..., s6) are linearly...

Consider the multiple regression problem including an intercept with the following list of explanatory variables:

for i = 1,... ,N.

a) Show that the last six variables (c4, s4, ..., s6) are linearly dependent on the first six (c1, s1, ..., s3) and an intercept.

b) Test whether the regression software that you commonly use can detect dependencies among the explanatory variables, using 3.1416 as your approximation for π, and various values of N.

c) Repeat this exercise with a cruder approximation 3.14 for π or a more precise one.

d) Repeat this exercise with 4 in place of 7 (that is, 2πi/4, 4πi/4, etc.).