statistics regression project rev a1

8/8/2019 Statistics Regression Project REV a1

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Statistics Regression Project

By Joseph Higgins

The purpose of my study was to compare the height of people to the resting pulse

rate of their hearts. The independent variable in my study was height. The dependent

variable in the study was their resting pulse rates. Height was measured in inches, andresting pulse rates were measured in beats per minute. My hypothesis about the

correlation between height and resting pulse rate is that the taller a person is the higher I

thought their resting pulse rate would be. I felt this way since taller people have longer veins and arteries and presumed that caused the heart to work harder. I gathered my

sample from a friend that works in a local hospital emergency room. The population

used was the patients of that emergency room.

Data- (63,68),(65.7,80),(63.8,84),(68.9,80),(72.8,80), (63.8, 80), (68.1, 92), (65.7, 92),

(66.9, 80), (66.9, 80), (64.2, 80), (62.2, 80), (61.8, 80), (63, 78), (66.9, 90), (69.7, 80),

(65.4, 72), (66.9, 80), (58.3, 82), (68.9, 76), (63, 84), (60.2, 70), (72.8, 80), (65, 82),

(65, 84), (67.7, 116), (72.8, 80), (64.2, 95), (69.7, 80), (65, 76), (71.7, 100), (63.8, 88),(67.7, 90), (69.7, 90), (66.1, 90), (70.1, 80), (71.7, 76), (65.7, 80), (66.9, 84), (63, 80),

(71.7, 80), (66.1, 80), (61, 80), (68.9,104), (66.1, 80), (70.9, 68), (68.9, 84), (57.1, 64),(66.9, 84), (68.9, 72).

Height vs Pulse Rate

ŷ= 0.5324x + 46.937

R2 = 0.0475

6065707580859095

100105110115120

50 52 54 56 58 60 62 64 66 68 70 72 74

Height in Inches

P u l s e R a t e p e r M

i n u t e

Series1

(x-bar, y-bar)

Linear (Series1)

Explanation :The correlation between my data is positive. I found that often times taller people had

higher resting pulse rates, but as this was not always the case I found the relationship

weak.



The result for the correlation coefficient is r = .217483, which suggests a very weak

strength and direction of the linear correlation. As the height increases it does not

necessarily accompany a higher resting heart rate. The correlation coefficient for asample size of 50 is at α = 0.05, is .279, and at α = 0.01, is .361. At the 5% significance

level there is not enough evidence that the height of a person would be significant enough

to equal a higher resting pulse rate; because .216<.279. Likewise, there is not enoughevidence at the 1% level that the height of a person would be significant enough to equal

a higher resting pulse rate; because .216<.361. The coefficient of determination is r² = .

0475. This means that 4.75% of the variation of y can be explained by the relationship between x and y. The remaining 95.25% of the variation is unexplained and is likely due

to other factors or to sampling error. The equation of the regression line is ŷ = 0.5324x +

46.937; the slope indicates that as the height increase that the hearts’ resting pulse rate

would increase .5324 beats per minute, and the y intercept when at a height of 0’’ would be 46.937 beats per minute when in a resting state. The outliers are listed at: (67.7,116),

(65.78,92),(66.9,90),(67.7,90),(60.2,70),(63,68),(68.9,72) ,(70.1,80),(69.7,80),(72.8,80),

this might be because I was only taking into account the height of a person and the

resting pulse per minute, and not taking into account the general health of the person. TheExtrapolate data point for example would be if I pick someone that’s 82’’ tall, which is

currently out of my data set; so ŷ = 0.5324(82) + 46.937 = 90.48 beats per minutes whenat a resting state. The interpolate data point for example would be if I pick someone in

my data, so 67.7 for my x-value would be ŷ = 0.5324(67.7) + 46.937 = 82.901 which

would be 83 beats per minute when at a resting state. The data does not match the value

that was recorded for that data set y = 116.

In conclusion, my data did not support my hypothesis. In the beginning I thought

that it would be a causal relationship based from what I learned in anatomy, thinking thelength of the veins would contribute to a higher heart rate. I thought taller people having

longer veins would always have a higher heart rate also. Confounding variables that

might have affected my data for this correlation study were: viscosity of the blood, and peripheral resistance; these factors could add in impedance to the flow of blood due to

friction between the blood and the walls of the vessels. Some other confounding variables

that were not taken into consideration with this study were the general health overall of the subjects. For example, if a person exercises, or if they have other health risks like

hypertension that would lead to a higher resting pulse rate. Next, the reason why they

went to the ER in the first place was not taken into account, this could have also affected

the resting pulse rate of a person if they were in the ER for a condition that issymptomatic of higher rates. One bias that could have been present in this study would

be “undercoverage” since the study did not include the “whole” population of the

hospital. The study did include the whole population for one night of the ER room. Thenon-response is the other bias that could have been present, due to a nurse physically

taking the peoples’ heights, and resting pulse rates. The response bias would not have

affected this study, due to the fact that people therefore could not lie about their height, or their resting heart rate since the nurses and machines were measuring the information.

Lastly, there weren’t any leading questions to cause a bias about the peoples’ heights and

their resting pulse rates.

statistics regression project rev a1

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