Consider the multiple linear regression model

y = 0 +1x1 +2x2 +3x3 +4x4 +

Using the procedure for testing a general linear hypothesis, show how to test

a. H 0 : 1 = 2 = 3 = 4 =

b. H 0 : 1 = 2 , 3 = 4

The answer for a. is

(Using Tb = c)

T = (0 1 -1 0 0 B= (B0 C = (0

0 0 1 -1 0 B1 B

0 0 0 1 -1) B2 B

B3 B

B4) B)

I think we need show or we somehow know that B1 = B2 , B2=B3, B3=B4 =0 , B1-B2 = 0 , B2-B3=0 and B3-B4=0

Does this equation help too Y0=B0

Y1= B1(=B2=B3=B4)

Z1 = X1 + X2 + X3 +x4

somehow substituiting should give us Y=y0+y1Z1 + epsilon

How do we get this answer? I do not understand the steps taken.

The answer for b. is we use B from part a, c = (0

0)

and the answer is T=(0 1 -1 0 0

0 0 0 1 -1)

Again, I do not understand how we got this.