Analysis
Assignment #2

50
points

Due:
December 11^th, 2016 11:59 p.m.

Student
Name: ______________________________

Submission
Date: _________________

Instructions:

Rename this file as first initial_lastname_assignment2_mmddyyyy.
Provide your answer underneath each question. You must upload the renamed file
with your answer to the Assignment 2 tab inside the class Blackboard by the
deadline.

1.
In
a sample of 140 hospitalized older adults, the individuals were
cross-classified by their cognitive impairment status and whether they had an
incidence of fall, and an association was tested between the two classification
factors.(6 points)

	Fall?	Total
Yes	No
Cognitive Impairment?	Yes	Count % (within impairment) % (within fall)	10 25.0% 50.0%	30 75.0% 25.0%	40 100.0%
No	Count % (within impairment) % (within fall)	10 10.0% 50.0%	90 90.0% 75.0%	100 100.0%
Total	Count % (within impairment) % (within fall)	20 14.3% 100.0%	120 85.7% 100.0%	140 100.0% 100.0%

Chi-square
(df=1) = 5.25, p-value = 0.022

Answer the following questions based
on the data above.

a. What percentage of
elders in this sample had a fall? (2 points)

I.14.3%

II. 20.0%

III. 25.0%

IV. 85.7%

b. Is there an evidence of
association between cognitive status and incidence of fall? Support your answer
with a statistic.(2 points)

c. Compute expected frequency
for the cell with cognitive impairment and fall.(2 points)

2.
The
following correlation matrix represents relationships among social variables.
These data were obtained from 793 children in the third, fourth and fifth
grades in 10 different elementary schools. For each of the variables a higher
score indicates more of the attribute.(6 points)

Table 1:
Correlation matrix (Pearson’s correlation coefficient)

Variable	1	2	3	4	5	6	7	8
1. Withdrawal	1.0
2. Aggression	-.10	1.0
3. Social Preference	-.39	-.44	1.0
4. Victimization by peers	.42	.53	-.68	1.0
5. Number of affiliative links	-.35	.05	.35	-.21	1.0
6. Loneliness	.29	.12	-.34	.34	-.18	1.0
7. Perceived social acceptance	-.27	-.04	.28	-.26	.18	-.69	1.0
8. Perceived behavior-conflict	.06	-.32	.17	-.17	-.06	-.35	.39	1.0

a.
What
is the value of the Pearson’s r for the relationship between “withdrawal” and
“aggression”? Interpret the value in words. (2 pts)

b.
Which
variable has the strongest relationship with “withdrawal”? (2 pts)

c.
What
is the value of the coefficient of determination for the relationship between
perceived behavior conflict and social preference? (2 pts)

3.
The
following table shows the relationship between methyl mercury intake (ug Hg/day)
and whole blood mercury values (ug/g) in 12 subjects exposed to methyl mercury
through consumption of contaminated fish.(8 points)

Table 2: Linear
regression of whole blood mercury on methyl mercury intake through contaminated
fish

Model	Unstandardized Coefficients	Standardized Coefficients	Sig.
B	Std. Error	Beta
1 (Constant) Methyl Mercury Intake	-20.579 0.641	30.662 0.074	0.940	0.517 <0.001

N = 12,
F = 75.53 (p < 0.001), R²
= 0.883

a.
Write
a research question for this scenario. (2 pts)

b.
Write
the estimated regression equation describing the linear relationship between
the two variables. (2 pts)

c.
Interpret
the coefficient of determination value. (2 pts)

d.
If
someone had a methyl Mercury intake of 500 units, what would be the amount of
mercury in the whole blood? (2 pts)

4.
Refer
to the data on cardiovascular risk factors (RISKFACT). The subjects are 250
males engaged in sedentary occupations. You wish to study the relationships
among risk factors in this population. The variables included are: (7 points)

Y= oxygen consumption
X1 = systolic blood pressure (mm Hg)
X2 = total Cholesterol (mg/DL)
X3 = HDL cholesterol (mg/DL)
X4 = triglycerides (ug/DL)

Table 3: Linear
regression of oxygen consumption on four independent (explanatory) variables

Model	Unstandardized Coefficients	Standardized Coefficients	Sig.
B	Std. Error	Beta
1 (Constant) Systolic BP Total cholesterol HDL Triglycerides	-8.131 0.333 -0.173 0.528 0.068	2.806 0.023 0.006 0.020 0.005	0.525 -0.983 0.759 0.385	0.004 <0.001 <0.001 <0.001 <0.001

N = 250,
F = 314.02 (p < 0.001), R²
= 0.837

a.
Using
all the variables, write a research hypothesis for these data. (2 pts)

b.
Write
out the multiple regression equation for these data. (2 pts)

c.
Interpret
the effects of Systolic BP and total cholesterol variables. (2 pts)

d.
What
is the most relevant predictor in the model? (1 pt)

5.
Research
suggests that both maternal smoking history and maternal BMI are associated
with the delivery of low birth weight infants. In the table below, birth weight
(grams) and BMI are continuous variables and smoking history is a categorical
variable. The research question is: Does the infant mean birth weight differ by
maternal smoking status after controlling for maternal BMI? (7 points)

Table 4: Analysis of
covariance results

Smoking History	N	Adjusted Means (SD) Birth Weight in Grams	F-Ratio and p-value	Multiple Comparisons Current Smokers Past Smokers
Current Smokers	30	2,802.84 (645.0)	F = 8.36 (p=.028)
Past Smokers	30	3,183.95 (592.2)	p = .037
Never Smokers	30	3,236.91 (576.3)	p = .011	p = .752

Levene’s
test p-value = 0.968

Linear
relationship between infant birth weight and maternal BMI, r = -0.20, p<.001

Homogeneity
of regression assumption p>.05

a.
In
the research question above: (3 pts)

i. What is the dependent
variable?

ii. What is the independent
variable?

iii. What is the covariate?

b.
Is
the homogeneity of regression assumption met? Provide statistical evidence. (1
pt)

c.
Is
there a statistical evidence of group difference? If yes, what is the evidence?
(1 pt)

d.
After
reviewing the multiple comparisons section of the table, identify which groups
differ significantly and which ones do not differ significantly from each
other. In each comparison state whether the mean birth weight is higher or
lower for each group. (2 pts)

6.
These
data are from a Prostate Cancer Study data set, with a sample of 379 men. A
logistic regression model was fit to the data with capsule penetration
(CAPSULE) as the dependent variable with predictor variables of age (Age),
prostatic specific antigen (PSA), and tumor volume (VOL). The dependent variable is coded as 0= no
capsule penetration and 1 = capsule penetration. The independent variables are
all continuous variables. The data for this study are presented in the table
below. (8 points)

Clinical variables that may predict
capsule penetration

	B	SE (B)	Odds Ratio	Sig.	95% CI, Odds Ratio
Lower	Upper
Constant	-0.493	1.137	0.61	.665
Age	-0.006	0.017	0.99		.961	1.028
PSA	0.051	0.009	1.05	.000	1.033	1.072
VOL	-0.016	0.007	0.98	.016	0.971	0.997
	N = 379, Nagelkerke R2 = 0.183 Hosmer-Lemeshow Chi-square = 8.463,df= 8,p= .390

a.
Write
a research hypothesis for these data. (2 pts)

b.
How
would you interpret NagelkerkeR²
value? (2 pts)

c.
Is
age a significant predictor in the model? Why or why not? Provide statistical
evidence. (2 pts)

d.
Interpret
effect of PSA and VOL in words. (2 pts)

7.
Suppose
that a researcher conducted a prospective cohort study, i.e. they followed a
number of participants over 10 years in which they started with known exposure
(smoking status), and recorded lung cancer diagnosis (outcome) at the end of
the study. They classified participants by smoking status and lung cancer
diagnosis as follows: (8 points)

Outcome Risk factor	Lung cancer	No lung cancer
Smoker	200	950
Nonsmoker	15	1575

a.
Compute
risk of lung cancer in smoking group. (2 pts)

b.
Compute
risk of lung cancer in nonsmoking group. (2 pts)

c.
Estimate
relative risk. (2 pts)

d.
How
would you interpret the relative risk estimate? (2 pts)