Association of Body Mass Index With Blood Pressure

NB: We do not resell your papers. Upon ordering, we do an original paper exclusively for you.

NB: All your data is kept safe from the public.

MAT 135 Project One

Population and selection of response and explanatory variables

Target Population	People with obesity
Studys explanatory variable	Body mass index
Studys response variable	Systolic blood pressure

Description of relationships

The body mass index has a strong positive relationship with systolic blood pressure among individuals. Obesity is a significant risk factor for hypertension because fat deposits restrict the blood flow in arteries and increase blood pressure. Moreover, obesity changes the metabolic mechanism of blood sugar regulation, absorption of ions by kidneys, and hormonal levels, resulting in increased blood pressure among obese individuals. The body mass index is an appropriate parameter for measuring weight because it considers the height of individuals. In this case, the study hypothesizes that an increase in body mass index causes a significant increase in systolic blood pressure.

Collected data

Individual Number	Body Mass Index	Systolic Blood Pressure
1	31	125
2	37	142
3	30	124
4	35	136
5	36	132
6	34	131
7	32	135
8	40	145
9	39	143
10	35	136
11	32	132
12	34	134
13	36	138
14	36	135
15	35	138
16	32	133
17	38	139
18	37	131
19	34	135
20	32	132
21	31	136
22	35	132
23	33	134
24	39	143
25	38	142
26	37	141
27	35	138
28	36	137
29	34	134
30	32	131

Descriptive Statistics

Table 1 offers a summary of descriptive statistics of body mass index and systolic blood pressure. The body mass index of individuals has a mean of 34.8, mode of 35.0, and median of 35.0. As the measures of spread, the body mass index has a range of 10 with a maximum value of 40 and minimum one of 30, a standard deviation of 2.6, and variance of 6.9. Systolic blood pressure has a mean of 135.5, median of 135.0, and mode of 132. The range of systolic blood pressure is 21 with a maximum value of 145 and minimum one of 124 with a standard deviation of 5.0 and variance of 24.7.

Table 1: Descriptive Statistics of Body Mass Index and Systolic Blood Pressure

	Body Mass Index	Systolic Blood Pressure
Mean	34.8	135.5
Median	35.0	135.0
Mode	35.0	132.0
Standard Deviation	2.6	5.0
Sample Variance	6.9	24.7
Range	10.0	21.0
Minimum	30.0	124.0
Maximum	40.0	145.0
Count	30.0	30.0

Graphs

Histograms of body mass index (Figure 1) and systolic blood pressure (Figure 2) show that their data follow the normal distribution. In body mass index, most individuals were between 34 and 36, while in systolic blood pressure, the group of 134-136 had the highest frequencies.

Figure 1: Histogram showing distribution of individuals based on body mass index

Figure 2: Histogram showing the distribution of individuals based on systolic blood pressure

Linear regression

Scatterplot of my data

The scatterplot (Figure 3) shows that the systolic blood pressures have a linear relationship with body mass index because of the consistent trend of data points. Additionally, the linear relationship is a positive one since the systolic blood pressure increases with the rise in the body mass index.

Figure 3: Scatterplot showing distribution of data points

Correlation

Correlation outcomes (Table 2) show that the body mass index and systolic blood pressure have a strong positive relationship (r = 0.803). The correction coefficient implies that systolic blood pressure rises as the body mass index increases among individuals. Since body mass index is an explanatory variable, it has a positive influence on systolic blood pressure among individuals. Linderman et al. (2018) aver that body mass index is a causal factor of hypertension among individuals. Therefore, the strong relationship confirms that body mass index in people with obesity contributes to high blood pressure.

Table 2: Correlation between body mass index and systolic blood pressure

	Body Mass Index	Systolic Blood Pressure
Body Mass Index	1
Systolic Blood Pressure	0.803	1

The linear regression equation for my data.

Regression coefficients (Table 3) indicate that a unit increase in the body mass index causes the systolic blood pressure to increase by 1.52 units. Hence, the following is the linear regression equation:

Systolic blood pressure = 82.51 + 1.52 (systolic blood pressure)

Table 3: Regression Output

Regression Statistics
Multiple R	0.803
R Square	0.645
Adjusted R Square	0.632
Standard Error	3.016
Observations	30

ANOVA
	df	SS	MS	F	Significance F
Regression	1	462.708	462.708	50.855	0.000
Residual	28	254.758	9.099
Total	29	717.467

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	82.506	7.447	11.079	0.000	67.252	97.760
Body Mass Index	1.520	0.213	7.131	0.000	1.084	1.957

The meaning of the y-intercept from part c means in terms of your two variables.

The y-intercept in the regression equation means that the systolic blood pressure would be 82.51 when the body mass index is zero.

The meaning of slope

The slope of the regression equation shows is a positive relationship where a unit increase in the body mass index makes the systolic blood pressure to increase by 1.52 units.

Scatter plot with the regression line (Figure 4):

Two random individuals (Table 4):

Table 4: Residual values of two random variables

Explanatory value	Estimated response value	Actual response value	Residual value
32	131.15	133	1.85
38	140.27	142	1.73

Description of results and assumptions

The analysis of the relationship between variables matches the assumption of the study that an increase in body mass index causes a significant increase in systolic blood pressure. The scatterplot shows a trend of data points depicting a positive relationship between the body mass index and the systolic blood pressure. The regression output (Table 2) confirms that the body mass index has a strong relationship with the systolic blood pressure (R = 0.803). It also reveals that the body mass index accounts for 64.5% of the variation in the systolic blood pressure in people with obesity. The regression model used is statistically significant in predicting the impact of body mass index on the systolic blood pressure among people with obesity, F(1,28) = 50.86, p = 0.000. The regression coefficient shows that a unit increase in the body mass index results in an increase of the systolic blood pressure by 1.52 units among people with obesity.

Reference

Linderman, G. C., Lu, J., Lu, Y., Sun, X., Xu, W., Nasir, K.,& & Krumholz, H. M. (2018). Association of body mass index with blood pressure among 1.7 million Chinese adults. JAMA Network Open, 1(4), 1-11.

Click Here To Order Now!