Modeling the Relationship Between Calories and Activity Metrics: A Regression Analysis with Variable Selection

Physical activity monitors have become integral to daily routines, with wearable devices such as the Apple Watch and Fitbit offering continuous data on users’ physical activity. This study compares the measurement accuracy of these devices by examining how they record parameters relevant to fitness and health. Employing multiple linear regression, we modeled the relationship between calories expended and a set of explanatory variables, including heart rate, steps, distance, age, activity level, weight, and device type. Evaluation of all possible variable combinations identified heart rate, steps, distance, weight, and watch type as the most effective predictors of calorie expenditure. Although the selected model demonstrated strong performance based on model selection metrics, several key regression assumptions were violated; specifically, the residuals exhibited non-normality, curvature, and heteroscedasticity, and seven influential observations were detected. The limited sample size further restricts the generalizability of the findings. Future research should focus on enlarging the dataset and exploring transformation techniques to better meet regression assumptions. These results provide valuable insights for consumers and researchers regarding the comparative accuracy of wearable devices in measuring physical activity and highlight methodological challenges that warrant further investigation.