Question

Q1. Consider the linear regression model y=β

0
​
+β
1
​
x
1
​
+β
2
​
x
2
​
+ϵ. 1(5). The residuals are listed below: 0.2,0.3,−0.8,−0.8,−0.3,0.4,0.1,−0.1,−0.4,−0.7,0.6,−0.1,−0.1,0.3,0.2. Do a Durbin-Watson test H
0
​
: the error terms are not (first-order) autocorrelated. H
a
​
: the error terms are negatively or positively (first-order) autocorrelated. Let α=0.1 2(5). The residuals are: 0.2,0.3,−0.8,−0.8,−0.3, calculate e
(i)
​
,z
(i)
​
and construct the normal plot.

Answer 1

Explanation:

To determine the optimal solution among the three potential solutions A, B, and C, we need to evaluate the objective function value (Z) for each solution and select the one with the minimum value.

Solution A = (0, 70):

Z_A = 10(0) + 6(70) = 420

Solution B = (5, 60):

Z_B = 10(5) + 6(60) = 370

Solution C = (50, 0):

Z_C = 10(50) + 6(0) = 500

Comparing the objective function values, we find that the minimum value is achieved at Solution B, which has an objective function value of 370. Therefore, the optimal solution is B = (5, 60) with Z = 370.