CE 160, Linear Regression
Assume we have a set of data, consisting of pairs of points (x,y).
The ith data point is denoted by (xi,yi)
We decide to fit a linear model to the data, which can be expressed as,
y' mx b
(1)
The unknowns in the equation are m an
Linear Regression
180
160
140
120
100
Y
Data
80
60
40
20
0
0
20
40
60
X
80
100
120
n
m
b
R
R2
9
sum X
408
X
3
5
10
12
32
54
78
102
112
sum y
659
y
2
9
14
45
82
101
121
131
154
sum xy
48857
xy
6
45
140
540
2624
5454
9438
13362
17248
sum x2
33250
x2
9
25
10
n
m
b
1.31105188
15.1160806
m
b
0.19325405
29.5996002
8
sum X
sum y
296
X
3
5
10
12
32
54
78
102
509
y
6
9
14
45
82
101
121
131
n
sum xy
31621
xy
18
45
140
540
2624
5454
9438
13362
sum x2
20706
x2
9
25
100
144
1024
2916
6084
10404
8
sum X
sum y
296
X
3
5
CE 160
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Grading Scale: CE 160, Fall 2015
Exams are 100% of your class score. Extra credit is given for completing the teaching
evaluation at the end of the semester.
There will be 2 exams during the semester.
Except under very rare circumstances, I do not give ma
CE 160 Exam Reference Materials Allowed and Required
Exams in CE 160 are hands-on using Excel. I will give you problems to
do in Excel and your excel file will be your test.
You can bring any printed or written material to use as reference
material during
CE 160, Exam #2, Fall Semester 2015
The date and time you need to be present in Town Engineering
106 for exam #2 is shown below. Note there is one exam time for
each section, the exam will be during finals week and the exam
will be in Town Engineering 106
Page 1 of 2
CE 160 Overview
Instructor:
LaDon Jones
416B Town Engineering
[email protected]
In CE 160 you will be introduced to the use of Microsoft Excel for performing engineering computations
and presenting the results. Topics to be covered include:
1
CE 160
Civil Engineering Example for Excel
The Manning Equation
The Manning Equation is used to estimate surface water flow in an open
channel.
The Manning equation is:
Q
1.49
AR 2 / 3S1 / 2
n
where
A is the cross-section area of flow, ft2
P is the wett
CE 160
Determine the System Head (hs) for the following conditions, for
Q(ft3/s) =1,10,15,20,25,30,35,40,45,50
Where:
pipe diameter = 3 feet
Pipe length = 2500 feet
Manning roughness = 0.013
Minor loss coefficient (values, bends, etc.): k = 8
Static lift
CE 160
Determine the System Head (hs) for the following conditions, for
Q(ft3/s) =1,10,15,20,25,30,35,40,45,50
Where:
pipe diameter = 3 feet
Pipe length = 2500 feet
Manning roughness = 0.013
Minor loss coefficient (values, bends, etc.): k = 8
Static lift
Cross-Section area and wetted perimeter for a pipe with a depth of water, y.
y
z
r
x
y
r
Area of an arc of radius r with angle .
=
2
2
=
When = 2
= 2
= 2
cos() =
= cos 1 ( )
2 + 2 = 2
= 2 2
y
x
r
y
z