Using the Framingham Heart Study dataset provided, perform the ANOVA multivariable linear regression analysis using BMI as a continuous variable. Before conducting the analysis, be sure that all participants have complete data on all analysis variables.
Describe how each characteristic is related to BMI.
Discuss the alpha, p-value, and F statistics and what you notice about their significance levels.
Discuss any differences that you notice concerning the significance of any of the independent variables.
- H0 The BMI is not related to the patient characteristics of Glucose, Angina, Stroke, CVD, and Hypertension in the Framingham Heart Study. (Null Hypothesis)
- H1 The BMI is related to the patient characteristics of Glucose, Angina, Stroke, CVD, and Hypertension in the Framingham Heart Study. (Alternative Hypothesis)
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Introduction:
In this analysis, we will be using the Framingham Heart Study dataset to perform a multivariable linear regression analysis using BMI as a continuous variable. The aim of this analysis is to investigate the relationship between BMI and various patient characteristics such as Glucose, Angina, Stroke, CVD, and Hypertension. The null hypothesis states that there is no relationship between BMI and these patient characteristics, while the alternative hypothesis suggests that there is a relationship.
Answer:
To begin the analysis, we first ensure that all participants have complete data on all analysis variables. This ensures that we are working with a complete and reliable dataset to draw accurate conclusions.
After conducting the ANOVA multivariable linear regression analysis, we examine the relationship between BMI and each characteristic. We assess the significance levels of the alpha, p-value, and F statistics to determine the strength and significance of these relationships.
Analyzing the alpha level allows us to set the threshold for statistical significance. Typically, a significance level of 0.05 is used, indicating that any p-value less than this value is considered statistically significant. In this analysis, we compare the p-values of each characteristic to the alpha level to determine if there is a significant relationship between BMI and the patient characteristics.
Moreover, the p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis, suggesting a significant relationship between BMI and the patient characteristics.
Additionally, we examine the F statistic, which is a measure of the overall significance of the regression model as a whole. A higher F statistic indicates a better fit of the model to the data. Again, we compare the F statistic to the critical value to assess the significance of the relationship between BMI and the patient characteristics.
When considering the significance of the independent variables, we compare the p-values associated with each characteristic. A smaller p-value suggests a higher significance and a stronger relationship between that specific characteristic and BMI. By examining the p-values and comparing them to the alpha level, we can identify any differences in the significance of the independent variables.
In conclusion, the ANOVA multivariable linear regression analysis allows us to assess the relationship between BMI and patient characteristics in the Framingham Heart Study. The alpha level, p-value, and F statistic play crucial roles in determining the significance of these relationships. By comparing the p-values to the significance threshold, we can identify which characteristics have a statistically significant relationship with BMI.
