Simple Linear Regression Model
Objective:
The correlation between food environment and health outcomes is tested in three different parts. In the previous sections (t-test & ANOVA test), we failed to find any signficant effect of the food environment to the health outcomes at the county level. In this section, we are trying to use the simple linear regression model to see if we can find find any statistical evidence of the correlation of the food enviroment and health outcomes. The model will have the dependent variable, health outcomes (obesity rate and diabetes rate), and one independent variable, food environment (fast food ratio). We run two separate regressions for the two health outcomes.
Regression on Obesity Rate:
Specification: Obesity Rate = beta0 + beta1 (Fast Food Ratio) + e
Regression on Diabetes Rate:
Specification: Diabetes Rate = beta0 + beta1 (Fast Food Ratio) + e
| Report | Obesity Rate | Diabetes Rate |
|---|---|---|
| Coefficient | 0.0002 | -0.00025 |
| Intercept | 30.849 | 10.084 |
| R^2 | 0.0233 | -0.0631 |
| p-value | 0.2645 | 0.00245 |
| Standard Error | 0.00018 | 0.00008 |
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Conclusion:
Again, we failed to find any statistical evident from the two regressions suggest any correlation between food environment and health outcomes. However, this result does not suggest the food environement has no correlation with the health outcomes at the county level. There are at least two logical reasons for further study in this topic. First of all, the simple linear regression model failed to control other factors that could possibly contribute to the "Obesity Epidemic", such as education, population demographic, work environment, etc. Without controlling these factors, it is very reasonable to believe that the simple linear regression model has an omitted variable issue. Secondly, food environment is constructed based on business decision. Most fast food restaurant chains target a particular population (usually low income family), so it is possible that the county income distribution is correlated with both the food environment and health outcomes at the same time.