Homework 10
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School
Georgia Institute Of Technology *
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Course
2400
Subject
Health Science
Date
Dec 6, 2023
Type
docx
Pages
5
Uploaded by BrigadierHummingbirdPerson940
Name:
Rebecca Fisher
Collaborators
1
: Beth Patterson
Basic information
Topics covered: Logistic regression.
Assigned: 11/14
Due: 11/21
Data notes: No external data is needed to answer the questions.
Submission: Please submit via Canvas. Submit one word or pdf file, with each problem starting on a new
page.
Put all code, figures, and work in the word/pdf document.
1
Please list anyone you worked with on the homework. This uses the honor system. Remember that I
encourage you to work together but that the work your turn in should be your own work.
Problem 1:
Suzuki et al. (2006) measured sand grain size on 28 beaches in Japan and observed the presence or
absence of the burrowing wolf spider Lycosa ishikariana on each beach. Sand grain size is a
measurement variable, and spider presence or absence is a nominal variable.
At what grain size, the odds of seeing a spider is 1 to 3.
If the sand grain size is increased 0.05 mm, how will the odds of seeing a spider be affected, explain your
work.
a)
Equations:
Odds= P/(1-P) = 1/3
Ln[Y/(1-Y)]= β
0
+ β
1
x
1
X
1
= (ln(P/1-P) - β
0
)/ β
1
Calculations:
Logistic regression in excel (x-var= grain size, y-var= spiders(presence)
X
1
= ln(1/3) +1.255/ 4.40927
.0355
Analysis:
At a grain size of .0355mm the odds of seeing a side is 1/3
b)
Equations:
Estimated regression equation:
P
=
e
B
0
+
B
1
x
1
1
+
e
B
0
+
B
1
x
1
Calculations:
Logistic regression in excel with all sizes+.05 mm (x-var= grain size +.05, y-var= spiders(presence)
P= =
grain
¿¿
¿
−
1.6476
+
5.1215
¿
1
+
e
¿
e
−
1.6476
+
5.1215
(
grainsize
)
¿
grain size =.0355
.2109
Analysis:
In the shifted model the odds of seeing a spider at grain size .035 decreased to about 1 to 5.
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Problem 2:
Insulin on Opossum Liver.
Corkill (1932) provides data on the influence of insulin on opossum liver. In the experimental setup the
20 animals (common gray Australian opossums — Trichosurus) fasted for 24 or 36 hours. Ten animals,
four from the 24-hour fasting group and six from the 36-hour fasting group, were injected with insulin,
while the remaining ten animals served as controls, that is, they received no insulin. After 3 to 4 hours
liver glycogen and blood sugar were measured. The weights of the animals were recorded as well. The
goal of the study was to explore the deposition of liver glycogen after the insulin regimen in opossums.
In rabbits and cats, for example, it was previously found that insulin induced significant glycogen storage.
This study found a slight depletion of liver glycogen after the insulin treatment. Our goal is to model the
liver glycogen based on weight, level of blood sugar, insulin indicator, and fasting regime. Is the insulin
indicator (0 no, 1 yes) an important covariate in the model?
Hypothesis:
H
0
=
the insulin indicator is not an important covariate to the liver glycogen
level.
H
1
=
the insulin indicator is an important covariate to the liver glycogen level.
Testing:
Logistic Regression Test on excel (x-var= liver gly, y-var= insulin)
Liver Glycogen= β0+β1×Weight β2×Blood Sugar+β3×Fasting Period+β4×Insulin Indicator+ϵ
Analysis:
The P-value for insulin indicator(.066415) is
> .05, therefore we fail to reject the null hypothesis:
showing
insulin indicator is not an important covariate to the liver glycogen
The P-value for Fast Period(.001) < .05; indicating statistically significant relationship between
fast period & liver glycogen.
The r-squared value is .656, which shows a moderate-high level of correlation