Need help with parts e through f. I have already found the following:

SST: 2,844

SSM: 1,922

SSR: 2,680.3047619047625

SSE: 163.69523809523753

SSTm: 158

SSRm: 964.9714285714293

The least square estimate for b: [2.19047619, 3.79047619, -1]

estimate for ²: 10.9130133333

Test statistic F(R): 81.8687646893

Currently stuck on how to test H0 : b = 0 against H1 : b 0 and constructing the 90% confidence interval. The given design matrix X is 18x3, has full rank of 3, so we have 18 observations.

1. Consider the model y=Xb+e,eN(0,2I) Here, b=b0b1b2 X is the design matrix, y the observed values of the yi, X=111111111111111111000111222333444555112112112112112112,y=154323431017168201615202118 (a) Find SST,SSR,SSE. (b) Find SSTm,SSRm,SSM. (c) Find the least square estimate for b. (d) Find the estimate for 2. (e) Test H0:b=0 again H1:b=0. (f) Construct the 90% confidence interval for b0. (g) Construct the 90% confidence interval for b0+b1+b2