# Tag Info

1 vote

### Given a predictor $x$. under what circumstance would you have high $R^2$ but low $\beta$

Let's consider a regression relationship between, say, driving time $y$ and distance travelled $x$: $$y = x\beta + e$$ $x$ is denominated in kilometers, just for fun. Now, let's rescale $x$, so that ...
• 40.5k
1 vote

### Model has higher (and closer to 1) $\beta$, but similar $R^2$ and correlation

The evaluation criteria $R2$ is equivalent to square error $SE=\sum(y-\hat{y})^2$, so I will replace $R2$ with simpler $SE$ for the remaining part. The $\beta_1=0.8$ is problematic as it shows that ...
1 vote

### Can I use a simpler model (small R²) to get more statistically relevant results?

Study statistical principles and use subject matter knowledge to pre-specify a model that makes sense, adjusting for things that should be adjusted for. Then don’t handle missing values in an ad hoc ...
• 95.6k

Only top scored, non community-wiki answers of a minimum length are eligible