CEE 304 - UNCERTAINTY ANALYSIS IN ENGINEERING
letHomework #12 Due: Monday Nov. 26, 2007, in class.
Read:
§ 12.1-12.5, and § 13.1-13.2, 13.4 (through Devore7 p. 540
[Devore6 p. 600].
)
This assignment is worth 200 points
rather than regular 100 because of extra question
Q-2 – Data for this problem is on Blackboard under ‘Assignments’.
Goal:
Regression is a widely used statistical technique. Whenever one wants to model or explore the
relationship between one variable, and one or more explanatory variables, regression analysis is the tool. You
should learn about the basic issues and models employed in a standard linear regression analysis, how to
compute estimators of parameters and the residual mean square error, to interpret the results of the analysis
(including R
2
) and to explain the results, and to test if coefficients are significantly different from zero (or other
values), as well as to construct confidence intervals for: parameters, a future observation, or the mean of future
observations. We will analyze rigorously a simple model with one explanatory variable (Chapter 12) and
discuss (without derivation) the analysis of linear models with several explanatory variables (Chapter 13).
Assignments
ActivStats Lessons (Optional)
:
On page 24-1 view activity Two (“Use the Statistics”) and activity Four (“Know the
Assumptions”). STUDY QUESTION:
What are the 4 key assumptions?
Devore and Other Problems
Section 12.1, Devore7 p. 454 [D6 p. 505 ] #9abcd
Section 12.2, Devore7 p. 466 [D6 p. 518] #18abcd
Section 12.3, Devore7 p. 475 [D6 p. 528] #31
Section 12.3, D36ab. [from Devore 5
th
edition]
An article in the
Journal of Public Health Engineering
reports the results of a regression analysis
based on
n
= 15 observations in which
x
= filter application temperature (°C) and
y
= %
efficiency of BOD removal.
Calculated quantities include
x
i
=
402
"
,
x
i
2
=
11,098
"
,
s
=
3.725,
and
ˆ
#
1
=
1.7035
.
a.
Test at level .01
H
0
:
β
1
=1
which states that the expected increase in %BOD removal is
1 when filter application temperature increases by 1°C, against the alterative
H
a
:
1
>1.
b.
Compute a 99% CI for
1
, the expected increase in % BOD removal for a 1°C increase
in filter application temperature.
Section 12.4, D45ab [from Devore 5