Multiple Linear Regression, Interpolation, and Numerical Integration
Homework #8
CIVL 3103
Due Tuesday, December 2
1. The electric power consumed each month by a chemical plant is thought to be
related to the average ambient temperature, x1, the number of days in the month
x2, the average product purity, x3, and the tons of product produced, x4. The past
year’s historical data are available and are presented in the table below.
a. Fit a multiple linear regression model to these data.
b. Perform a residuals analysis using graphical methods discussed in class
(you do not have to plot a normal curve on the histogram of your
residuals).
c. Test for the significance of the regression at α = 0.05.
d. Use the t-test to assess the contribution of each regressor to the model.
Using α= 0.05, what conclusions can you draw?
Y
240
236
270
274
301
316
300
296
267
276
288
261
X1
25
31
45
60
65
72
80
84
75
60
50
38
X2
24
21
24
25
25
26
25
25
24
25
25
23
X3
91
90
88
87
91
94
87
86
88
91
90
89
X4
100
95
110
88
94
99
97
96
110
105
100
98
2. Consider the data in the table below. Use interpolation to find the value of the
constant-pressure specific heat (Cp) at a temperature of 1238 K. Use a first order,
second order, and third order polynomial. Which polynomial do you think is
most appropriate for interpolation of this data? Explain your answer.
T, K
1000
1100
1200
1300
1400
1500
Cp, kJ/kg-K
1.410
1.1573
1.1722
1.1858
1.1982
1.2095
3. Evaluate the following integral using both the Trapezoid and Simpson’s 1/3 rule
with n = 1, 2, 4, and 8 subintervals for Trapezoid and n = 2, 4, and 8 subintervals
for Simpson’s rule. Compare these results to the exact solution.
10
 (5x
0
4
 4 x3  2 x  3)dx