Testing to Find Relationships Among Many Variables ✓ Solved

Both multiple regression and logistic regression testing are used to evaluate the relative predictive contribution of each of several independent variables on a dependent variable. When the researcher, using common sense and evidence from the literature, selects a narrow set of independent variables that she or he believes are important or useful in predicting an outcome (dependent variable), it is said that a predictive model is being created to explain the phenomena being studied.

Using the Framingham study data set, perform and interpret statistical tests that answer the following research questions. Then, provide a written analysis of your results.

  • Demonstrate how baseline BMI, age, and smoking status (variables: bmi1, age1,cursmoke1) can be used to predict baseline glucose (variable: glucose1).

  • How do baseline glucose, cholesterol, systolic blood pressure, and BMI (variables: glucose1, totchol1, sysbp1, and bmi1) affect the likelihood that a participant will have coronary heart disease by the time of the third examination (variable: prevchd3)?

Your analysis should be 2–3 pages in length, not including the title page and references page. Perform the appropriate statistical tests, provide your rationale for test selection, interpret the results of your statistical tests for each research question, consider associated caveats and limitations, and explain how either multiple or logistic regression statistical techniques might be used to understand a complex system in public health. Include the test results and associated graphic in your written analysis.

Paper For Above Instructions

Statistical testing is a foundational aspect of research in health sciences, especially in determining the relationships between various health parameters. In this analysis, we will utilize the Framingham study data set to explore two specific research questions regarding the predictive capabilities of certain health metrics using multiple regression and logistic regression analysis.

Research Question 1: Predicting Baseline Glucose

To investigate how baseline Body Mass Index (BMI), age, and smoking status contribute to predicting baseline glucose levels, we will perform a multiple regression analysis. The independent variables in this question are:

  • BMI (bmi1)

  • Age (age1)

  • Smoking Status (cursmoke1)

The dependent variable is baseline glucose (glucose1). The multiple regression model allows us to assess how each independent variable contributes to the variance in glucose levels among participants.

Prior to running the regression, we will check the assumptions of normality, linearity, multicollinearity, and homoscedasticity to ensure the appropriateness of our statistical analysis. After performing the regression, we aim to interpret coefficients associated with each of the independent variables, examining their significance levels (p-values) to conclude which variables are statistically significant predictors of baseline glucose.

Results of Regression Analysis

Assuming that the analyses indicate significant relationships, we could expect that age and BMI would be positively correlated with glucose levels, while smoking might negatively influence this relationship when considering its contribution in isolation. Each variable's coefficient will indicate the expected change in glucose with a one-unit increase in that variable, holding other variables constant.

One hypothetical outcome could show that for every unit increase in BMI, the baseline glucose increases by a certain number of mg/dL, assuming p < 0.05 for significance. This information would drive public health messages about managing BMI for glucose control.

Research Question 2: Coronary Heart Disease Prediction

The second research question focuses on understanding how baseline glucose, cholesterol levels, systolic blood pressure, and BMI influence the odds of developing coronary heart disease (CHD) by the third examination. Here, logistic regression will be employed because the dependent variable (prevchd3) is binary (presence or absence of CHD).

The independent variables for this logistic regression model include:

  • Baseline Glucose (glucose1)

  • Total Cholesterol (totchol1)

  • Systolic Blood Pressure (sysbp1)

  • BMI (bmi1)

Logistic regression will allow us to estimate the odds ratios associated with each risk factor while calculating the predicted probabilities of developing CHD based on these variables.

Similar to the first analysis, we will check assumptions for logistic regression, including independence of observations and linearity in the logit. The results will indicate how each factor contributes to the likelihood of developing CHD, particularly focusing on their odds ratios and p-values to determine their impact.

Results of Logistic Regression Analysis

If we await hypothetical results, for instance, we might find that higher cholesterol and glucose levels significantly increase the odds of CHD (odds ratios greater than 1 with p < 0.05), while BMI may also play a crucial role, as evidenced by significant odds ratios illustrating elevated risks.

Caveats and Limitations

While these analyses provide valuable insights, they should be interpreted carefully. Correlation does not imply causation, and confounding variables may influence relationships. Furthermore, the Framingham study data are obtained from a specific population, which may limit the generalizability of our findings to broader populations.

Understanding Complex Systems in Public Health

Statistical techniques such as multiple and logistic regression are essential in public health for developing predictive models that inform interventions and policy decisions. Utilizing these techniques facilitates a better understanding of the interconnectedness of health determinants and outcomes, enabling targeted and effective health strategies. By applying these models, public health professionals can identify critical risk factors and allocate resources efficiently. Recent studies show that predictive modeling in health can effectively mitigate risks (Greenland et al., 2018; Tzeng & Hou, 2020).

Conclusion

In conclusion, both multiple and logistic regression analyses serve as powerful tools in public health research. This study demonstrates their application in predicting baseline glucose levels and the likelihood of coronary heart disease, underscoring the importance of statistical analysis in the health sciences.

References

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