Copy of 2024_Winter_PH 7B HW1.docx
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Feb 20, 2024
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PH 7B Public Health Statistics II
Homework 1
Question 1 (5 pts):
Which of the following correlation coefficients shows the
weakest
relationship?
A.
0.68
B.
-0.05
C. 0.50
D. -0.96
Explain:
The weakest relationship is -0.05 because the more a correlation is near to 0 the more
it shows the weaker relationship
Question 2 (5 pts):
True or False: If y is usually less than x, the correlation coefficient between
x and y will be negative.
True or False: False
Explain:
This is false because if x and y have a positive linear relationship the correlation
coefficient will be positive so it’s a possibility for y to be less than x and still have a positive r
value.
Question 3 (5 pts):
When exchanging x and y, the scatter plot will look ________, and the
correlation coefficient will be _______, and the slope of the regression line will be________.
A.
Different, the same, different
B.
Different, the same, the same
C. The same, different, the same
D. The same, the same, different
Explain:
The correlation coefficient indicates the direction of the relationship (positive or
negative), and will remain the same after swapping the variables.
PH 7B Public Health Statistics II
Homework 1
Question 4 (5 pts):
The scatterplot below shows the regression line between height and body
weight. The average height is 70 inches, SD= 3 inches; the average weight is 180 pounds, SD=
45 pounds, r=0.40. What does the check mark with the green arrow represent?
Explain:
The green check mark represents the expected weight for an individual who is 1 SD
above average in height. (1 SD above the individual height)
PH 7B Public Health Statistics II
Homework 1
Question 5 (15 pts):
The table below records the minutes of exercise per day and hours of
sleep during weekdays and weekends in a research study.
(keep one decimal place)
Participant ID
Weekdays
Weekends
Exercise
(min)
Sleep
(hours)
Exercise
(min)
Sleep
(hours)
1
40
7
65
7
2
80
9
45
8
3
75
8
75
6
4
60
7
80
9
5
45
8
50
7
Mean=60,
SD=15.8
Mean=7.8,
SD=0.7
Mean=63,
SD=13.6
Mean=7.4,
SD=1.0
1)
Find out the correlation coefficient between hours spent on exercise and hours of sleep
during weekdays and weekends, respectively.
Show your work.
r= 0.7 and r=0.1
2)
On what days (weekdays or weekends), hours spent on exercise is more strongly
correlated with hours of sleep? Why?
Weekdays are a stronger correlation because 0.7 is closer to 1
3)
The same group of participants all decided to extend 20 minutes of exercise everyday
during weekdays and double the amount of their exercise time on the weekend.
However, they found out their sleep time still remained the same. Calculate the new
correlation coefficients for both groups and explain how it differs from the previous
schedule.
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PH 7B Public Health Statistics II
Homework 1
Both groups stayed the same after adding 20 and doubling the amount of exercise because the
correlation coefficients did not change due to the same number being added to both variables.
Question 6 (15pts):
There was a health study among the senior population in Orange County,
where a large group of individuals have their systolic blood pressure (SBP) measured at age 60
and again at age 70. The following results are obtained.
Age 60: average SBP = 135 mmHg, SD=5 mmHg
Age 70: average SBP = 140 mmHg, SD=5 mmHg
r=0.80
1)
Estimate the average SBP at age 70 for all the individuals who had SBP of 140 mmHg at
age 60.
0.80x(5/5)=0.8
140-0.80x125=32
32+0.80x140=144mmHg
2)
Predict the SBP at age 70 for an individual who had SBP of 130 mmHg at age 60.
32+0.80X130=136mmHg
3)
Another person aged 60 from New York City, with an SBP of 150 mmHg, would like to
know his systolic blood pressure in 10 years based on your research results. Would you
be able to help him calculate it? If so, write down your prediction. If not, explain why.
32+0.80x150=152mmHg