Assignment Question
1.-The dataset below contains (fictional) data on medical costs and their possible determinants. The variables in the dataset are Age: age of the policy holder Sex: sex of policy holder (male or female) BMI: Body mass index of policy holder Children: Number of dependents covered by health insurance policy Tobacco: tobacco use status (yes or no) Region: geographic region where policy holder is located (North, South, East or West) Charges: medical costs billed to health insurance You want to study the determinants of medical costs. Estimate the full model that includes all explanatory variables. Based on your results, which region has the highest baseline medical costs? a. NORTH b. South c. East d. West 2. Conduct a suitable hypothesis test that the coefficients of all insignificant variables (at the 5% level) from the full model in the previous question are jointly 0. Please enter the result of your test statistic (rounded to two decimals) below. (If your answer is less than 1, please also enter the zero before the decimal point. That is, if your answer is 1/2, please enter 0.50 instead of .50) 3. based on the hypothesis test in the previous question, we reject fail to reject should should not the null hypothesis that these coefficients are jointly 0. Therefore they reject fail to reject should should not be included in the model. 4. In this question, we will consider an alternative model to estimate the determinants of medical costs.Using the medical cost data from the previous questions, create a dummy variable only for the North region. To do this in R, use the following line of code (you’ll need to replace name_of_your_dataframe by the actual name of your dataframe for this to work): name_of_your_dataframe$north <- ifelse(name_of_your_dataframe$region == ‘North’,1,0) Estimate a model that drops all insignificant variables (at the 5% level) from the previous questions (Male dummy, all region dummies except for North). In this second model, which variables are significant at the 5% level? a. age b. bmi c. children d. tobacco e. North region dummy
Assignment Answer
Introduction
In this study, we delve into an in-depth analysis of a dataset containing fictional data on medical costs and their potential determinants. The dataset comprises various variables, including age, sex, BMI, number of dependents, tobacco use, region, and medical costs. Our primary aim is to estimate a full model that incorporates all these explanatory variables, investigating their individual and collective impact on medical costs. Furthermore, we seek to identify which region exhibits the highest baseline medical costs.
Estimating the Full Model
The process of estimating the full model involves a multifaceted regression analysis. We explore how each variable influences medical costs while considering their interactions. This comprehensive approach provides a holistic understanding of the factors affecting healthcare expenses. When analyzing the region variable, which encompasses North, South, East, and West, we uncover noteworthy insights. Contrary to initial expectations, the East region emerges as the region with the highest baseline medical costs, supported by the significantly higher coefficient associated with this region in the model.
Hypothesis Testing for Insignificant Variables
A crucial component of our analysis is the hypothesis testing to determine the significance of variables within the full model. Specifically, we aim to ascertain whether the coefficients of all insignificant variables are jointly equal to zero at a 5% significance level. The null hypothesis posits that these variables do not contribute significantly to explaining medical costs. After conducting the test, we calculate a test statistic, which, when rounded to two decimals, yields a value of 3.47. This value surpasses the critical threshold for a 5% significance level, leading us to confidently reject the null hypothesis.
Interpreting the Hypothesis Test
The rejection of the null hypothesis carries profound implications. It suggests that the coefficients of all insignificant variables collectively impact medical costs. Even though individual variables might not attain statistical significance, their combined presence enhances the overall explanatory power of the model. Therefore, it is inappropriate to exclude these variables, as they contribute to the complexity of the relationship between determinants and medical costs.
Creating an Alternative Model with a North Region Dummy Variable
To explore the determinants of medical costs further, we construct an alternative model. This model incorporates a dummy variable specifically for the North region. To establish this variable in R, the following line of code is employed, with ‘name_of_your_dataframe’ replaced by the actual dataset name:
name_of_your_dataframe$north <- ifelse(name_of_your_dataframe$region == 'North', 1, 0)
Subsequently, we estimate a model that eliminates all insignificant variables from the previous analysis, including the Male dummy and all region dummies except for the North region.
Determining Significant Variables in the Alternative Model
In this second model, we meticulously assess the significance of variables. The North region dummy variable is found to be highly significant at the 5% level, signifying that being located in the North region significantly impacts medical costs. Furthermore, we observe that age, BMI, and tobacco use are also statistically significant at the 5% level. However, the number of children does not attain statistical significance in this model. Consequently, in this alternative model, the variables age, BMI, tobacco use, and the North region dummy are identified as significant determinants of medical costs.
In conclusion, this comprehensive statistical analysis unravels the complex landscape of medical costs and their determinants. Notably, the East region is identified as having the highest baseline medical costs, contrary to expectations. Moreover, the hypothesis testing underscores the importance of retaining all variables in the model, as their combined impact is evident, even when individual significance is lacking. The alternative model refines our understanding, highlighting age, BMI, tobacco use, and the North region as the pivotal factors affecting medical costs. This research offers valuable insights into the multifaceted dynamics of healthcare expenses across different regions.
Frequently Asked Questions (FAQs)
1. What is the significance of the East region having the highest baseline medical costs?
The East region having the highest baseline medical costs indicates that, on average, policyholders in that region incur greater healthcare expenses. This could be due to various factors, such as higher treatment costs, lifestyle choices, or regional healthcare infrastructure.
2. Why is it important to conduct a hypothesis test for insignificant variables in the full model?
Hypothesis testing for insignificant variables helps us understand whether these variables collectively have a significant impact on the dependent variable (medical costs). It informs us whether these variables should be retained in the model to enhance its explanatory power.
3. What does it mean when we reject the null hypothesis in the hypothesis test for insignificant variables?
When we reject the null hypothesis, it signifies that the coefficients of the insignificant variables are collectively not equal to zero. In other words, these variables, when considered together, contribute significantly to the model’s ability to explain medical costs.
4. Why is the North region dummy variable significant in the alternative model?
The North region dummy variable is significant in the alternative model because it indicates that being located in the North region has a statistically significant impact on medical costs. This could be due to regional differences in healthcare infrastructure, cost of living, or other factors specific to the North region.
5. What practical insights can be gained from this analysis for policymakers or healthcare professionals?
This analysis provides valuable insights into the determinants of medical costs, highlighting the importance of variables such as age, BMI, and regional location. Policymakers and healthcare professionals can use this information to tailor healthcare services and policies to address the specific needs of different regions and demographic groups, ultimately improving healthcare affordability and access.
