**Decoding VIF and R-Squared: A Deep Dive into Regression Analysis**

Greetings, fellow data enthusiasts!

Today, let’s delve into some nuances of regression analysis:

**Unraveling VIF**:

VIF, or Variance Inflation Factor, is our torchbearer in the dark alleys of multicollinearity. A lofty VIF signals that a predictor might be echoing the song of other predictors a bit too loudly. Let’s dissect our models:

– **Model A**: Alarmingly, our constant has soared to a VIF of 325.88, hinting at some entanglement with other variables, which raises eyebrows about the model’s foundation.
– **Model B**: This model, albeit slightly better with a VIF of 318.05, still poses concerns. It’s armed with predictors like inactivity and obesity percentage.
– **Model C**: With a VIF of 120.67 for the constant, it’s still on the higher side but better. This model is anchored by inactivity and diabetes percentage.

**The Tale of R-Squared**:

The R-squared value is akin to a storyteller. It narrates how much of our dependent variable’s story is told by our predictors. Here’s our story:

– **Model A**: With an R-squared of 0.125, it tells us that our duo of diabetes and obesity percentage unravels about 12.5% of the plot.
– **Model B**: Climbing a tad to 0.155, inactivity and obesity percentage reveal around 15.5% of the mystery.
– **Model C**: At 0.093, inactivity and diabetes shed light on roughly 9.3% of the tale.

**Intercepts, Coefficients, and Their Tales**:

The intercept is our starting point, our baseline. Coefficients, on the other hand, narrate the change. To name a few from our roster:
– **Model A**: Begins at -0.158, with diabetes and obesity adding 0.957 and 0.445 to the tale respectively.
– **Model B**: Starts at 1.654, with inactivity and obesity chipping in with 0.232 and 0.111.
– **Model C**: Embarks at 12.794, and inactivity and diabetes contribute 0.247 and 0.254 respectively.

**Deciphering Confidence Intervals**:

These intervals are our safety nets. They tell us where our predictions are likely playing. For instance, Model A’s diabetes percentage dances between [0.769, 1.145] with 95% confidence.

**The Dance of F-Statistic**:

This metric evaluates our model’s harmony. A minuscule p-value for the F-statistic is music to our ears, confirming our model’s rhythm. Gratifyingly, all three models have hit the right notes with significant F-statistics.

Stay tuned for more insights as we continue our journey through the realm of data!

Best,

Aditya Domala