VIF values:
VIF (Varian Inflation Factor) values measure the degree of multicollinearity between the independent variables. A high VIF indicates a strong correlation between the predictor and other predictors. Here are the interpretations of your models: Model A: the constant (const) has a very high VIF value (325.88), indicating multicollinearity with other variables in the model. This indicates potential problems with model stability and interpretability. Model B: Like Model A, Model B has a high VIF (318.05) for the constant, but it is slightly lower. This model includes inactivity and percent obesity as predictors. Model C: Model C has a lower but still higher VIF of constant (120.67) and includes inactivity and percent diabetes as predictors.
R-Square (Average R-Square):
R-squared (coefficient of determination) measures how well the independent variables explain the variance of the dependent variable. A larger R-square means a better fit to the data. The R-squared for Model A is 0.125, indicating that approximately 12.5% of the variance in the dependent variable is explained by the percentage of diabetes and obesity. The R-squared for Model B is slightly higher at 0.155, suggesting that approximately 15.5% of the variance in the dependent variable is explained by the percentage of inactivity and obesity. The smallest R-square for Model C is 0.093, indicating that only about 9.3% of the variance in the dependent variable is explained by the percentage of inactivity and diabetes.
End point and probability:
The intercept represents the predicted value of the dependent variable when all independent variables are zero. Coefficients represent the change in the dependent variable for a one-unit change in the independent variable. In Model A, the intercept is -0.158 and the coefficients for percentage of diabetes and obesity are 0.957 and 0.445. For model B, the intercept is 1.654 and the coefficients for inactivity and obesity percentage are 0.232 and 0.111. For model C, the intercept is 12.794, and the coefficients for percentage inactivity and diabetes are 0.247 and 0.254.
Confidence intervals:
Confidence intervals provide a range of values within which you can expect the probabilities to be at a certain level of confidence (eg 95%). Narrower ranges indicate greater accuracy. For example, in model A, the 95% confidence interval for percent diabetes is [0.769, 1.145], which means you can be 95% sure that the true percent diabetes is in this range.
F-Statistic and Prob (F-Statistic):
The F-statistic tests whether the overall model fits the data well. A small p-value (Prob (F-Statistic)) indicates that the model is statistically significant. In all three models, the F-statistic is highly significant (very small p-values), indicating that the models as a whole are statistically significant.