BME 230B: Applied Engineering Mathematics
Department of Biomedical Engineering
University of California, Irvine
January 16, 2018
HOME WORK 1 | Basic Statistics
Download the data le "data01.txt" from the course website. This le contains
a table of measurements related to the volumes of speci c compartments of the hu-
man head from a recent study in healthy and pathological aging (e.g., Misra et al.,
NeuroImage 2009, 1415-1422).
The 10 columns are denoted as:
ID: A subject identi er
SEX: The sex of the subject (F = female, M = male)
AGE: The subject’s age [in years]
WEIGHT: The subject’s weight [in kg]
GRP: The clinical group that a subject was assigned to (CTRL = control, MCI
= patient with minimal cognitive impairment, AD = patient with Alzheimer’s
disease).
SMO: If a subject is a smoker
HAND: Handedness of a subject
GMV: The volume of the brain’s grey matter [in ml], (roughly, the neurons)
WMV: The volume of the brain’s white matter [in ml], (roughly, the ber bun-
dles connecting the neurons)
CSFV: The volume of the cerebrospinal uid [in ml], (i.e., the uid compartment
inside the skull)
Make sure that you understand the meaning and relation between the compartments,
e.g., note that the brain volume is BRV=GMV+WMV, and the intracranial volume
is ICV = CSFV+BRV. "NA" means that this item is not available.
Use statistical methods to address the following questions. Do not guess or "eye-
ball", but draw inferences from your analysis.
BME 230B Home Work 1 Winter 20181
Problem 1. [15%] Check data
Check the provided data for completeness and possible outliers & errors. You
may want to use histograms and plots here. Report if you decided to remove
data.
Problem 2. [15%] Sample description
Describe the study sample in terms of age, sex, and clinical grouping. Check
the age distribution of the sample. Is age balanced across sex and clinical
grouping?
Problem 3. [20%] In uence of a discrete variable
Does the brain volume (BRV) depend on smoking (SMO) or handedness
(HAND)? Interpret results and draw a conclusion.
Problem 4. [20%] In uence of a continuous variable
Do variables ICV, BRV, and the ratio BRV/ICV depend on age? Interpret
results and draw a conclusion.
Problem 5. [30%] Linear regression
a. Using linear regression, nd the set of independent variables that best
explain (1) the brain volume (BRV), (2) the grey matter volume (GMV), and
(3) the white matter volume (WMV). Report your best model only, but explain
the steps taken. Explain and interpret your ndings across all three models.
b. You may have noticed that there is a loss of compartment volumes BRV,
GMV, and WMV with age. Is the rate of this loss di erent between (1) sex and
(2) clinical grouping? (Hint: use a linear regression model with interactions
here). Report your best models only, but explain the steps taken. Explain and
interpret your ndings.
BME 230B Home Work 1 Winter 20182