Assignment07
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School
University of Northern Colorado *
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Course
602
Subject
Industrial Engineering
Date
Apr 3, 2024
Type
Pages
3
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SRM 602 Assignment 7
Note: You need to submit only Part II by the due date.
The HSB data set and its description, a readme file, are available in Canvas. You can also download
the R code for questions 5 and 6 from Canvas.
Part I: Problems from the text
: Do the problems 9.3, 9.9, 9.13 and 9.22 from the course
text book.
You could ignore the questions related to the omitted parts.
Part II: Questions
1.
A researcher conducts an experiment to examine the relationship between the weight gain
of chickens whose diets had been supplemented by different amounts of amino acid lysine and the
amount of lysine ingested. Since the percentage of lysine is known, and we can monitor the amount
of feed consumed, we can determine the amount of lysine eaten.
A random sample of twelve 2-
week-old chickens was selected for the study. Each was caged separately and was allowed to eat at
will from feed composed of a base supplemented with lysine. The sample data summarizing weight
gains and amounts of lysine eaten over the test period are given here. (In the data,
y
represents
weight gain in grams, and
x
represents the amount of lysine ingested in grams.)
Chick
y
x
Chick
y
x
1
14.7
.09
7
17.2
.11
2
17.8
.14
8
18.7
.19
3
19.6
.18
9
20.2
.23
4
18.4
.15
10
16.0
.13
5
20.5
.16
11
17.8
.17
6
21.1
.23
12
19.4
.21
(
a
)
Find the correlation coefficient between these two variables.
(
b
)
Find the equation of the least square line for these data and find the coefficient
of determination,
r
2
. Show your work.
(
c
)
Use the equation of the fitted line to predict the weight gain for a chicken who
had .2g lysine.
(
d
)
Give an interpretation of the cofficient of determination in the context of the
problem.
(
e
)
Calculate the residuals and SSE.
(
f
)
Draw the residual plot and describe your findings from this plot.
2.
Use R/SAS to verify the results you obtained in Problem 1.
1
3.
A company that manufactures spare parts experiences fluctuations in the lot sizes due
to fluctuations in supply and demand.
The company is interested in examining the relationship
between the number of man-hours worked and lot size. The number of man-hours worked is taken
as the dependent variable, where each (
X, Y
), combination represents one production run. Using
the data below, answer the following questions.
X:
30
20
60
80
40
50
60
30
70
60
Y:
73
50
128
170
87
108
135
69
148
132
(
a
)
Find the correlation coefficient between these two variables. Show your work.
(
b
)
Find the equation of the least square line for these data.
(
c
)
Find the coefficient of determination,
r
2
. Give an interpretation of the coefficient
of determination in the context of the problem.
(
d
)
Use the equation of the fitted line to predict the number of man hours worked
when the lot size is set at 55.
4.
Researchers are interested in assessing the relationship between the average number of
cigarettes smoked in a day,
X
, and systolic blood pressure,
Y
, among male smokers.
Using the
following data on
X
and
Y
answer the following questions.
X:
20
35
20
10
16
5
45
20
35
20
60
Y:
167
182
170
152
172
150
189
160
175
149
204
For this data set, SAS output below shows a regression analysis relating systolic blood pressure to
the average number of cigarettes smoked in a day.
(
a
)
Report the prediction equation, and interpret the slope.
(
b
)
Using the sample slope and the standard deviations, find the correlation. Interpret
its value.
(
c
)
Report
r
2
, and interpret its value.
(
d
)
Test the null hypothesis systolic blood pressure among male smokers is independent
of the average number of cigarettes smoked in a day, and report and interpret the P-value.
(
e
)
Construct a 95% confidence interval for
β
, and interpret.
2
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