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# Exploring Well-Being Factors with Statistics on BMI, Blood Pressure, and Age Using R Programming

In this comprehensive data analysis assignment, we delve into well-being factors utilizing statistical techniques and R programming. The assignment covers an array of topics, including the examination of BMI variations based on time spent in Australia, exploring the relationship between age and systolic blood pressure, and investigating correlations between time in Australia and hypertension. Through descriptive statistics, ANOVA, linear regression, and chi-squared tests, we reveal critical insights into these well-being aspects. This assignment showcases the power of data analysis in deciphering complex health-related data, with a particular emphasis on the skills of statistics and R programming.

## Problem Description

In the R Programming assignment, we delve into a dataset containing 60 observations and 6 variables gathered from the LWM-LMP program. Among these variables are three continuous ones: BMI, Systolic blood pressure, and Age, as well as three categorical variables: time spent in Australia, socioeconomic status, and the presence of hypertension. Our analysis will primarily emphasize the application of statistical techniques and the utilization of R programming to address key research questions.

## Part 1: Investigating BMI Across Time in Australia

Research Question: Is there a significant difference in the mean BMI among participants who spent varying durations in Australia, classified into five categories: >20 years, 1-5 years, 6-10 years, 11-20 years, and less than 12 months?

Analysis

We initiated our analysis with the calculation of descriptive statistics for BMI across the different time categories. The boxplot and a table of these statistics are presented below.

Variable Time Mean Std. Dev Variance Range
BMI >20 years 28.28 6.69 44.73 23.80
1-5 years 24.85 4.33 18.77 14.52
11-20 years 32.14 7.83 61.38 23.30
6-10 years 29.63 4.46 19.89 14.10
<12 months 27.38 5.96 35.54 21.99

Table 1: Descriptive Statistics for BMI by Time

Figure 1: Boxplot of BMI against Time

After observing the descriptive statistics and the boxplot, we noticed that there is no significant difference in BMI across different durations of time spent in Australia. However, two outlier points were identified - one in the '>20 years' category and another in the '<12 months' category.

Given these observations, we conducted an ANOVA test to assess whether there is a statistically significant difference in the average BMI across the different time categories. The null and alternative hypotheses were defined as follows:

• H0: μ1 = μ2 = μ3 = μ4 = μ5 (No significant difference)
• H1: At least one mean is different

The significance level was set at 5%. The ANOVA results are summarized in the table below.

Source of Variation DF Sum Sq Mean SQ F-Value P-value
Time 4 342.72 85.68 2.45 0.057
Residuals 55 1,923.05 34.97
Total 59 2,265.77 38.40

Table 2: Analysis of Variance for BMI by Time

The ANOVA test yielded a statistically significant result (F(4,55) = 2.45, p = 0.057). However, based on the significance level, it was concluded that the main effect of time is not statistically significant.

Conclusion

In conclusion, there was no significant difference in BMI among participants based on the duration they spent in Australia.

## Part 2: Examining the Relationship between Age and Systolic Blood Pressure

Research Question: Is there a linear relationship between systolic blood pressure and age, and is this relationship statistically significant?

Analysis

To address this question, we began by creating a scatterplot to visualize the potential linear relationship between age and systolic blood pressure.

Figure 2: Scatterplot of Age and Systolic Blood Pressure

The scatterplot suggested a weak linear relationship between age and systolic blood pressure. We proceeded to conduct a linear regression with systolic blood pressure as the dependent variable and age as the predictor.

The null and alternative hypotheses for the regression were defined as follows:

• H0: βage = 0 (No significant relationship)
• H1: βage ≠ 0

The significance level was set at 5%. The results of the linear regression analysis are displayed in the table below.

Coefficients Estimate Std. Error t-value P-value
Intercept 111.78 6.22 19.97 <0.001
Age 0.33 0.13 2.48 0.0162

Table 3: Linear Regression for Systolic Blood Pressure by Age

The linear regression model explained a statistically significant but weak proportion of variance (R2 = 0.10). The effect of age was statistically significant and positive (beta = 0.33, t(58) = 2.48, p = 0.016).

Conclusion

Based on the regression analysis, there was a weak, positive, and statistically significant relationship between age and systolic blood pressure.

## Part 3: Exploring Correlations Between Time in Australia and Hypertension

Research Question: Do the data provide evidence to suggest that the length of time spent in Australia (Time) is correlated with whether participants have hypertension?

Analysis

To address this research question, we used a chi-squared test of independence. Initially, we created a stacked bar chart to visualize the proportions of hypertension for each time category.

Figure 3: Stacked Bar Chart of Hypertension by Time

Based on the bar chart, there appeared to be some association between hypertension and time. The null and alternative hypotheses for the chi-squared test were defined as follows:

• H0: There is no association between time and hypertension
• H1: H0 is false

The significance level was set at 5%. The results of the chi-squared test are presented in the table below.

Time No Yes
>20 years 7 6
1-5 years 14 0
11-20 years 6 4
6-10 years 9 2
<12 months 9 3

Table 4: Chi-squared Test of Independence for Time and Hypertension

The chi-squared test yielded a statistically insignificant result (χ2 = 9.242, p = 0.055). The test indicated that the strength of association between time and hypertension was not strong enough to be considered significant.

Conclusion

Our analysis concluded that there was no significant correlation between hypertension and the time participants spent in Australia.

Summary

This assignment demonstrates the application of statistical methods and R programming skills to analyze data related to well-being. It showcases the use of descriptive statistics, ANOVA, linear regression, and chi-squared tests to address pertinent research questions related to BMI, systolic blood pressure, age, and their relationships with other variables.