Homework 9
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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
6
Uploaded by BrigadierHummingbirdPerson940
Name
:
Rebecca Fisher
Collaborators
1
:
Basic information
Topics covered:
Regression
Assigned:
11/07
Due:
11/14
Submission:
Please submit via Canvas. Submit one word file, with each problem starting on a
new page.
Put all code, figures, and work in the word document.
Notes:
We will deduct -.1 for each case of missing units.
Please round all ANSWERS to 2 decimal places or 3 places for p values
For problems 1 and 2, make sure to include:
o
Setup
: State (1) all assumptions, (2) test(s) to be conducted, (3) formulas used,
and (4) if appropriate the null and alternative hypothesis.
o
Calculation
: Calculate the test statistic(s) and the p value(s) or interval estimates.
o
Interpretation
: (1) state the result of your test using your hypotheses. (2) Explain
the result of your test in terms of what it means in the question context.
Problems
Problem 1:
BMI has been a gold standard for determining healthy weight. It is calculated from weight in
kilograms divided by the square of your height in meters.
One of the reasons that BMI has been
the gold standard is the ease of obtaining the required measures.
A clinical alternative is to determine body density based on underwater weighing techniques.
These immersion methods allow direct measurement of body fat, for which one such method is
described by Brozek.
(1) see whether height and weight are good predictors of the Brozek
percent body fat measurement in men. Description of columns below:
Variable
Description
id
Case Number
broz
Percent body fat using Brozek's equation, 457/Density - 414.2
density
Density (gm/cm^3)
age
Age (yrs)
weight
Weight (lbs)
height
Height (inches)
neck
Neck circumference (cm)
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.
chest
Chest circumference (cm)
abdomen
Abdomen circumference (cm) "at the umbilicus and level with the iliac crest"
hip
Hip circumference (cm)
thigh
Thigh circumference (cm)
knee
Knee circumference (cm)
ankle
Ankle circumference (cm)
biceps
Extended biceps circumference (cm)
forearm
Forearm circumference (cm)
wrist
Wrist circumference (cm) "distal to the styloid processes"
Immersion methods including Brozek’s method of measuring body fat are difficult and requires
specific hardware. A researcher would like to know if there are two factors that better predict the
Brozek percent body fat metric.
(2) By conducting a multiple regression analysis with all
independent variables, identify the 2 most significant factors that predict the Brozek percent
body fat metric and q determine if the reduced is different than the complete model.
We will deduct -.1 for each case of missing units.
Please round all ANSWERS to 2 decimal places or 3 places for p values
For problems 1 and 2, make sure to include:
o
Setup
: State (1) all assumptions, (2) test(s) to be conducted, (3) formulas used,
and (4) if appropriate the null and alternative hypothesis.
o
Calculation
: Calculate the test statistic(s) and the p value(s) or interval estimates.
Interpretation
: (1) state the result of your test using your hypotheses. (2) Explain the result of
your test in terms of what it means in the question context.
Part 1:
Assumptions:
Assume normal distribution
Assume weight & height are good tests of Brozak’s body fat measurement.
Hypothesis:
H
0
= Weight & height are significant indicators of body fat
H
1
= Weight & height are not significant indicators of body fat
Test:
Multi Regression Test on Excel
Conclusion:
P-value for weight and height is significantly less than .05, which shows that they
significantly affect the body fat measurement. Because p-value is less than .05, we do not reject
the null hypothesis. Therefore, weight & height are significant indicators of Brozak’s body fat
measurement.
Part 2:
Part 2a
Assumptions:
Assume linear distribution
Assume all variables have affect on body fat measurement.
Hypothesis:
H
0
= All variables are significant indicators of body fat
H
1
= All variables are not significant indicators of body fat
Test:
Multi Regression Test on Excel
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Conclusion:
P-value for intercept (representing all of the variables) = .34
^ is > .05 so reject the null hypothesis that all the variables are significant factors
Therefore, not all of the variables are significant indicators of body fat measurement.
Analysis:
The pvalue(showing significance) was very small Abdomen, Forearm, & Wrist.
The coefficient(showing intensity) was largest for Abdomen, Thigh, & Forearm.
Since Abdomen had high intensity & significance, it largest effect on the
b.f.measurement, more testing needs to be done to confirm which second has the largest effect.
Part 2b:
Assumptions:
Assume linear distribution
Assume abdomen has significant effect on body fat measurement.
Hypothesis:
H
0
= Forearm is a significant indicator of body fat
Wrist is a significant indicator of body fat
Thigh is a significant indicator of body fat
H
1
= Forearm is not a significant indicator of body fat
Wrist is a not significant indicator of body fat
Thigh is a not significant indicator of body fat
Test:
Multi Regression Test on Excel
Analysis:
Forearm p-value is > .05 = reject null hypothesis.
Pvalue for wrist(2.28E-08) & thigh(.007) < .05 = do not reject hypothesis
Wrist had the lowest p-value = highest significance
Conclusion:
Forearm is not a significant indicator of body fat
Wrist is a significant indicator of body fat
Thigh is a significant indicator of body fat
The abdomen & wrist measures are the most significant indicator for body fat
measurement.
Part 3
Assumptions:
Assume linear distribution
Assume abdomen & wrist are 2 most significant factors on body fat measurement.
Hypothesis:
H
0
= Abdomen & wrist are more significant factors than weight & height.
H
1
= Abdomen & wrist are not more significant factors than weight & height.
Test:
Multi Regression Test on Excel
Analysis:
Overall intercept pvalue for wrist & ab was .18
Overall intercept pvalue for weight & height was .0000101
W&H pvalue < Wrist & ab: reject null hypothesis
Conclusion:
Weight & height are more significant factors of body fat metric than abdomen &
wrist measurements.
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