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Ex 6.4
We assume Number of months after the most recent earthquake is 𝑋1 Number of
months after the second-most recent earthquake is 𝑋2.
(a) The regression model is Y = 166.91 + 1.23𝑋1−10.08𝑋2
(b) The 𝑅2 of my regression model is 0.52. Given the very imperfect nature of
earthquake prediction I think the 𝑅2 is high in this situation because there are lot
of factors contribute to the prediction of earthquake such as weather animal
behaviors and the years record can only serve as part of the reason. If we want to
get the 𝑅2 bigger we need to consider more factors.
(c) We can see that the P-value of 𝑋1 is larger than 0.05 so the variable cannot pass
the significant test.
(d) The smaller regression model is Y = 169.83 − 9.71𝑋2 the 𝑅2 is 0.51 and the p-
value of 𝑋2 is 0.009 it pass the significant test.
Ex 6.5
(a) The regression model is Y=-47.9+0.36X
(b) 𝑅2= 0.953, T -value = 23.93 P- value is much less than 0.05 according to the
three value the model is very good.
(c) But the residual plot has obvious patern that looks like a curve so the model is not
good.
(d) We sqaure root the X value then use it as 𝑋′ and Y to run regression finally I get
a residual plot without pattern. The new regression model is
𝑌 = −1.14 + 0.028 ∗√𝑋
𝑅2 = 0.988 T value = 48.7 P- value is much less than 0.05 so this regression model
is very good.
Ex 7.2
(a) 1. We define the decision variables
X: # of full-size microwave ovens company produce
Y: # of compact microwave ovens company produce
2. Construct the objective function
Company wishes to maximize the profit
Maximize:
120X+130Y
3. Construct the constraints
Ovens limited by GA:
2X + Y ≤ 500
Ovens limited by EA:
