Assume Alpha = 0.05 throughout this assignment

1. Using the matrix approach, construct the linear regression model of this dataset. (3 points)

i.e. y=B0+B1X1+B2X2+B3X3

2. Construct the 95% confidence interval of ₁.
3. Construct a 95% prediction interval on y, when (x1= 4, x2= 50, x3 = 1600)
4. Use the method of Extra sum of squares to test the following Hypothesis (H0:B1=B3=0) vs. at least one of B1, B3 is not equal to Zero
5. Find the standardized residual of the fourth observation.
6. Compute the Studentized residual which corresponds to the first observation (3, 45, 9)

Using the Cooks distance, does the first observation (3, 45, 9) have a significant impact on the use of the model? (Show calculations)

#### please answer EACH question clearly.

x1 1 1 1 2 3 4 WN 000 V - W NA x3 9 81 121 100 64 16 5 6 7 8 9 10 11 3 9 11 10 8 4 3 2 9 8 4 11 15 000 00 12 13 14 15 V 10.04 24.6 31 35.02 25.1 16 14.3 9.6 24 27 17.1 37.1 41.9 11.8 21.1 18.05 69.01 10.4 35 46.1 45.2 54.1 56 22.3 21.1 2 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 x2 45 110 122 530 295 200 375 52 101 302 412 404 500 377 205 400 600 585 540 250 290 510 590 100 410 16 17 18 19 20 21 22 23 24 25 26 2 4 4 4 20 1 10 15 15 16 17 6 6 9 4 4 81 64 16 121 225 4 16 16 400 1 100 225 225 256 289 36 36