Frontiers in Business, Economics and Management ISSN: 2766-824X | Vol. 18, No. 2, 2025 49 An Empirical Analysis of The Influencing Factors of America’s Medical Insurance Cost Tianyi Deng *, Shuai Gong, Wanlu Li, Tairan Zhou School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University (XJTLU), China * Corresponding author: Tianyi Deng (Email: Tianyi.Deng22@student.xjtlu.edu.cn) Abstract: This paper empirically analyzes the factors influencing the cost of medical insurance in the United States. Based on data from 12,761 American individuals sourced from Kaggle, the study examines the relationships between age, gender, body mass index (BMI), diabetes, smoking status, and medical insurance costs. Multiple linear regression models were employed, and model optimization techniques, such as log-linear transformation, were applied to enhance the explanatory power of the analysis. The results indicate that age, BMI, diabetes, and smoking status have significant positive correlations with medical insurance costs, while gender (female) shows a negative correlation. The final log-linear model achieved a high goodness-of-fit (R²=0.694), demonstrating that these factors effectively explain variations in medical insurance costs. The study provides valuable insights for insurance companies in premium pricing and for individuals in health management. Keywords: Medical insurance cost, BMI, Smoking status, Multiple linear regression, log-linear model. 1. Motivation Health insurance covers medical expenses incurred by individuals. It is a vital tool for individuals to manage the high expenditure of healthcare, and it is essential to ensure that people of all income levels have access to medical treatment. Ramachandran, Kavitha and Pandimeena (2023) emphasized that the effectiveness and provision of healthcare services must be improved to increase the productivity of human capital. World Health Organization (2021) reported that the cost of healthcare has been steadily rising worldwide between 2000 and 2018, accounting for almost 10% of global GDP. Moreover, Empirical data points to a link between insurance and economic expansion (Singhal, Goyal and Singhal, 2022). Consequently, given the social and economic significance of health insurance premiums, analyzing the factors that affect healthcare insurance costs is essential. Orji and Ukwandu (2023) claimed that this is essential for both luring and maintaining policyholders and effectively managing current insured. Indeed, actuarial modeling of insurance costs has emerged as a major field of study in the medical insurance industry in recent years (Duncan et al., 2016). Zhang (2019) employed a mediated effects model to investigate the relationship between environmental pollution and health insurance expenditures, revealing that environmental pollution substantially elevates medical insurance costs. He (2024) adopted the multiple linear regression model and the stepwise regression method, whose results reveal that age, BMI, number of children, smoker or non-smoker and region have plausible correlations with medical insurance cost. It is illustrated by Li (2021) that through the Dagum Gini coefficient method to a sample of 31 Chinese regions' statistics from 2010 to 2019, the amount spent on medical insurance funds varied by location. Using a logistic regression model, Zhou and Zhao (2022) demonstrated that customers who use the WeChat Healthcare pedometer function more frequently had lower rates of health insurance. Accurately developing a forecast model for medical insurance costs is difficult, nevertheless, because of the multiplicity of elements and their complexity (Orji and Ukwandu, 2023). Therefore, this paper utilizes econometric models to quantitatively examine the impact of age, BMI, diabetes, smoker and gender on the cost of medical insurance claims. Based on the analysis of these determinants, the article offers recommendations to both insurance companies and policyholders, to enable patients to make more informed decisions during medical treatments while allowing insurance companies to better to charge each customer an appropriate premium for the risk they represent, aiming to support the sustainable development of the health insurance industry. 2. Data Description 2.1. Source of Data This essay empirically explores the relationship between six variables and health insurance cost. Data was all aggregated from the Kaggle repository, which was collected by Suresh Gupta and contained 12761 entries from Americans. The 12761 individuals in the data used in this article all spent money on health insurance to some extent. They range in age from eighteen to sixty-four. The independent variables are age (A), gender (G), body mass index (BMI), diabetes (D), and smoker (S) and the dependent variable is medical insurance cost (MIC). 2.2. Description of the Variables 2.2.1. Medical insurance cost (MIC) Plemans (2024) stated that health insurance claims are formal requests made by policyholders to insurance companies for reimbursement of medical services they have received. The ability to predict a correct claim amount which is considered as the medical insurance cost has a critical influence on insurers for considering fixing the health premium to better manage and allocate health insurance funds. 2.2.2. Age (A) The risk of diagnosed diseases increases with age, older people usually tend to decline in physical function. Health insurance providers assess people based on age and offer health insurance premiums accordingly (Anderson et al., 50 2012). 2.2.3. Body mass index (BMI) BMI is defined as an indicator to measure obesity. A BMI over 24.9 is considered overweight and over 30 is considered obese. Xia (2023) revealed that, if a person's BMI is at a higher level, then that person will face a higher probability of transaction from health to death, and the cost of medical insurance claims is also higher. 2.2.4. Diabetes (D) Diabetes is a typical chronic disease, and patients need to invest in long-term medical expenses to maintain relative health of the body system. In recent years, the number of people with diabetes has increased, and the economic cost has also increased, mainly because having diabetes makes health insurance more expensive for that person (American Diabetes Association, 2018). 2.2.5. Smoker (S) According to epidemiological studies, smoking behavior will increase the probability of cancer, a serious threat to health (Yun et al., 2005). Consequently, smoking can raise the opportunity of developing certain medical disorders, and insurers may need to pay higher medical insurance costs for claims. 2.2.6. Gender (G) Males and females also have different physical conditions which means that the probability of diseases might vary by gender. Agnieszka (2020) claimed that women have greater medical needs for parturition and gynecological problems, so women's health insurance costs are higher than men's. Table 1. Description of the Variables Variable Description Unit Medical insurance cost (MIC) Medical cost of the client per year. The number of claims that insurance companies need to pay for the policyholders. US dollar Age (A) Present Age of the client Year Body mass index (BMI) 𝐵𝑀𝐼 𝑤𝑒𝑖𝑔ℎ𝑡 ℎ𝑒𝑖𝑔ℎ𝑡² kg/𝑚 Diabetes (D) No – 0, Yes – 1 None Smoker (S) No – 0, Yes – 1 None Gender (G) Male – 1, Female -0 None Source: Author-compiled 2.3. Descriptive Statistics The descriptive statistics for initial data and the relative. Table 2. Descriptive Statistics for Initial Data MIC A BMI D S G Observation 12761 12761 12761 12761 12761 12761 Mean 11591.45 39.63 30.04 0.77 0.15 1 SD 10018.61 14.06 6.05 0.42 0.36 0.50 Minimum 1121.90 18 16.00 0 0 0 Median 8964.10 40 29 1 0 0 Maximum 58571.10 64 53.10 1 1 1 Source: Author-compiled Figure 1. Relative Frequency of Variables 2.4. Data Processing The correlation between the variables is shown in Table 3. All five variables have a positive correlation with MIC, particularly age and smoking. This enables us to confirm that every variable in the model is statistically significant and to infer the relationships between the variables in a preliminary manner. More specifically, we examine the variance inflation factor (VIF) to test multicollinearity. Table 4 shows that the VIF values for all variables are close to 1, and the corresponding 1/VIF values range from 0.951 to 0.992, indicating that there 51 is no significant multicollinearity issue in the model. The variables are nearly independent, with a small linear correlation between them. This means each variable contributes independently to the model without interference, ensuring the model's stability. Therefore, there is no need to adjust the variables. Table 3. Correlation MIC A BMI D S G MIC Correlation 1 P-value A Correlation .377** 1 P-value 0.000 BMI Correlation .137** .192** 1 P-value 0.001 0.001 D Correlation .091** .069** .063** 1 P-value 0.001 0.001 0.001 S Correlation .694** -.018* -.061** .012 1 P-value 0.000 0.001 0.001 0.175 G Correlation .049** .017 .068** -.022* .070** 1 P-value 0.001 0.052 0.001 0.014 0.001 *p<0.05, **p<0.01, ***p<0.001 Source: Author-compiled Table 4. VIF Variable VIF 1/VIF A 1.040 0.960 G 1.010 0.989 BMI 1.050 0.951 D 1.010 0.992 S 1.010 0.991 Mean VIF 1.020 Source: Author-compiled 3. Empirical Model and Hypotheses 3.1. Hypothesis H0 (Null Hypothesis): β1=0 There is no significant relationship between the main variable and the dependent variable. H1 (Alternative Hypothesis): β1≠0 There is a significant relationship between the main variable and the dependent variable. 3.2. Hypothesis Testing for the Main Variable Based on the hypothesis test results from Table 5, Age is highly suitable as the main variable due to its statistically significant and strong relationship with MIC. The P-value for age is 0.000, allowing us to reject the null hypothesis and conclude that age has a significant impact on the dependent variable. Furthermore, the robust standard error of 5.845 and a high t-test value of 45.91 confirm the precision and strength of this relationship. From a theoretical perspective, it is also reasonable to expect that age could influence the dependent variable, as aging may correlate with higher health risks or insurance claim amounts. Table 5. Hypothesis test MIC Coefficient Robust Stand Error t-test P-value A 268.340 5.845 45.91 0.000 Constant 957.204 245.768 3.89 0.000 Source: Author-compiled 3.3. Model Selection Based on these findings, choosing the multiple linear regression model aligns well with the basic principles of econometrics, which state that maintaining the validity and integrity of the model's estimations depends critically on assigning the variable of interest nearly at random while holding the control variables constant. This method improves the study's analytical rigor and the findings' dependability, allowing for an objective and reliable age coefficient estimator. Additionally, it guarantees that the cost of medical insurance by age is interpreted causally. 3.3.1. Model 1 According to the result of hypothesis testing, we set age as the main variable. MIC=β0+β1A+β2BMI+β3D+β4G+ui, i=1, 2, 3...12761 MIC: dependent variable represents medical insurance cost A, BMI, D, G: Age, Body Mass Index, Diabetes and Gender, respectively ui: regression error β0: population intercept β1, β2, β3, β4: the corresponding coefficients for the independent variables Table 6. Model 1 Result Variable Coefficient Robust Stand error t- Statistic P-value A 256.340*** 6.099 42.03 0.000 BMI 101.323*** 13.866 7.31 0.000 D 1521.672*** 164.617 9.24 0.000 G 804.013*** 164.303 4.89 0.000 Constant -3177.339*** 439.881 -7.22 0.000 R-squared 0.152 Source: Author-compiled The results are promising, with the p-values for all variables being 0.000, indicating that the coefficients in the model are statistically significant. However, the R-squared value is relatively low, so the model has limited explanatory power. We believe this may be due to the omission of relevant variables. 52 3.3.2. Model 2 To enhance the model's goodness-of-fit and account for omitted causal effects that could lead to omitted variable bias, we draw on theoretical knowledge to hypothesize that smoking status may influence the medical insurance costs incurred by the insured. This is based on the premise that smoking increases the likelihood of developing certain diseases, which in turn could result in higher claim amounts. Furthermore, as observed in Table 3 and Table 4, although the correlation between Smoker and the existing independent variables is relatively weak, it is still meaningful from a statistical perspective. Furthermore, Smoker exhibits a strong and significant correlation with the dependent variable MIC. Therefore, the Smoker variable is introduced to attempt to reduce omitted variable bias and enhance the explanatory power of the model. MIC=β0+β1A+β2BMI+β3D+β4G+β5S+vi, i=1, 2, 3...12761 S: represent Smoker vi: the error term in model 2 β5: coefficient for Smoker Table 7. Model 2 Result Variable Coefficient Robust Stand error t- Statistic P-value A 260.554*** 3.875 67.25 0 BMI 178.595*** 9.093 19.64 0 D 1210.529*** 129.655 9.34 0 S 19988.93*** 237.944 84.01 0 G -248.301** 105.710 -2.41 0.016 Constant -8374.527*** 296.885 -26.48 0 R-squared 0.648 Source: Author-compiled After including the smoke variable, the R-squared value significantly improved and all variables remained statistically significant. This is a positive outcome, indicating that we have successfully identified and included an omitted variable. However, it is curious that the coefficients in the new model have increased substantially, with the smoker’s coefficients close to 20,000. Therefore, we began to explore the potential causes behind this issue. 3.3.3. Model 3 Figure 2. histogram of MIC Figure 3. histogram of Ln (MIC) When plotting the histogram of MIC, it becomes evident from Figure 2 that the majority of the data values are large, resulting in a right-skewed distribution. Right-skewed data typically contain extremely high values, which might inappropriately influence on the regression model, potentially leading to instability. According to theoretical principles, linear regression models assume that the error terms are normally distributed. However, skewed data generally fail to meet this assumption of normality. Benoit (2011) emphasized that one practical way to make a severely skewed variable more roughly normal is to apply logarithmic transforms. Subsequently, we applied a logarithmic transformation to the dependent variable. As shown in Figure 3, the transformed data now approximates a normal distribution. Therefore, to solve the issue we found in model 2, we introduce log-linear. Ln (MIC)=β0+β1A+β2BMI+β3D+β4G+β5S+vi, i=1, 2, 3...12761 Additionally, from the scatterplots, it can be observed that the model used in Figure 4 exhibits an uneven distribution of data points on either side of the fitting line, indicating the presence of bias or error patterns. In contrast, the model used in Figure 5 shows a more uniform distribution of data points around the fitting line, reflecting a more ideal-fitting performance with residuals that do not exhibit significant bias. Therefore, we have effectively applied the log-linear model. Table 8. Model 3 Result Variable Coefficient Robust Stand error t- Statistic P-value A 0.036*** 0.000 102.77 0.000 BMI 0.008*** 0.001 12.31 0.000 D 0.075*** 0.010 7.24 0.000 S 1.375*** 0.013 108.68 0.000 G -0.071*** 0.008 -8.42 0.000 Constant 7.095*** 0.023 307.95 0.000 R-squared 0.694 Source: Author-compiled 53 Figure 4. Scatter-plot of Model2 Figure 5. Scatter-plot of Model3 4. Regression Results and Inferences Our model iteration effectively increases the reliability of the estimators during the process of updating the three models, assuming that the estimations of the coefficients of age stay almost constant. Additionally, the final log-linear level of fit has significantly increased, going from 0.152 in model 1 to 0.694 in model 3. Observing more deeply into the coefficients from Table 8 reveals nuanced relationships between health insurance costs and personal characteristics. A and MIC have a positive link, and the coefficient is 0.036 (p<0.001) which indicates that people's medical needs typically increase as they age, leading to higher health insurance costs. For instance, older people may be more prone to chronic diseases that require more medical services and prescription drugs, so insurers need to charge higher premiums to cover those costs, considering the claim of healthcare insurance is higher. Additionally, BMI positively correlated with MIC (coefficient 0.008, p<0.001). An abnormal body mass index in real life will raise the incidence of certain illnesses, such as cardiovascular disease and diabetes. People with a higher BMI will pay higher premiums which are calculated by insurance providers because these health issues can result in more medical expenses and more insurance costs that insurers need to spend. Similarly, there is a positive correlation (0.075, p<0.001) between diabetes and medical insurance expenditures. Diabetes is a chronic disease that requires long-term treatment, including regular checkups, medication, and management of possible side effects. People with diabetes consequently pay more for healthcare. There is a high correlation between MIC and smoking behavior, as evidenced by the significant smoker coefficient (1.375, p<0.001). Smoking is a contributing factor to many hazardous diseases, including lung cancer and cardiovascular disease. Therefore, smokers might need more costly healthcare, insurance companies raise the premiums for smokers as they have a higher risk of paying more money on claims. The cost of medical insurance is lower for males than for females, as indicated by the negative correlation of -0.071 (p<0.001) between gender and medical insurance expenses in Model 3. The potential explanation could be that women have particular health requirements. For example, the costs associated with childbearing are high and include pregnancy testing, delivery, postpartum rehabilitation, and several other procedures that necessitate ongoing medical resource investment. Moreover, certain gynecological conditions, such as breast diseases and uterine fibroids, are more prevalent. In terms of the awareness of preventive health care, females might take the initiative to perform routine physical examinations, screening various diseases, and engage in other preventive medical behavior, so the frequency of women's medical treatment is relatively high, and the overall medical cost may be higher, which makes the insurance cost of women relatively higher than man, and there is a negative correlation with the male sex. 5. Conclusion and Discussion This essay analyzes the impact of age, BMI, diabetes, smoker and gender on the cost of medical insurance based on 12761 individuals from Americans. The study initially employed correlation analysis and VIF to assess the relationships between the independent variables and the dependent variable, as well as to identify whether there is potential multicollinearity among the factors. Subsequently, hypothesis testing was conducted on the primary variable, age, to validate its significant effect on the dependent variable. A multiple linear regression model was then applied, incorporating the control variable smoker to reduce omitted variable bias. Upon further analysis, it was observed that the dependent variable exhibited a right-skewed distribution with extreme values, which could compromise the stability of the model. To address this issue, the model was modified to a log- linear form. The results ultimately indicated that the log- linear model was the more suitable model for this study and these variables can be used to predict and explain medical insurance costs to a great extent. Despite the progress achieved in our study, certain limitations remain. After three iterations of model refinement, the R-squared of the model reached only 0.694, indicating that the fit still requires further improvement. This may be attributed to the current selection of variables—our analysis considered only five variables with MIC, overlooking other influential factors such as regional environment and social economic conditions. Furthermore, future research could explore the interaction effects among variables or apply more sophisticated models to enhance the explanatory power and predictive performance of the analysis. In addition, we have provided some practical recommendations for the two groups. For insurance companies, charging an appropriate premium based on the risk represented by each client is crucial. The ability to accurately predict claim amounts, or in other words, the health insurance costs, has a significant impact on the company's management decisions and financial statements. 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