RMSE vs R2

• RMSE tells us how far apart the predicted values are from the observed values in a dataset, on average. The lower the RMSE, the better a model fits a dataset.

  • The RMSE value tells us that the average deviation between the predicted house price made by the model and the actual house price is USD14,342.
  • It is calculated as $RMSE= \sqrt( \frac{1}{n}\sum(\hat{y_i}–y_i)^{2})$
  • $MSE=\frac{1}{n}\sum(\hat{y_i}–y_i)^{2}$

• R2 tells us the proportion of the variance in the response variable of a regression model that can be explained by the predictor variables. This value ranges from 0 to 1.

  • The higher the R2 value, the better a model fits a dataset.
  • The R2 value tells us that the predictor variables in the model are able to explain xx% of the variation in the values.
  • R Squared represents explained deviation from meanR Squared represents explained deviation from mean
    
    
    SSR represents expected deviation while SSE is the unexplained deviation
    
    SSR represents the expected (or explained) deviation from the mean. In another word, if we have a pre...

[!note]- Note on RMSE variables where:

• Σ is a symbol that means “sum”
• Pi is the predicted value for the ith observation
• Oi is the observed value for the ith observation
• n is the sample size

[!note]- Note on R Squared variables

• SSR represents the sum of squares of residuals
• SST represents the total sum of squares

• RMSE vs. R2: Which Metric Should You Use?

  • When assessing how well a model fits a dataset, it’s useful to calculate both the RMSE and the R2 value because each metric tells us something different.
  • One one hand, RMSE tells us the typical distance between the predicted value made by the regression model and the actual value.
  • On the other hand, R2 tells us how well the predictor variables can explain the variation in the response variable.

References

• RMSE vs. R-Squared: Which Metric Should You Use? (statology.org)

• [What is Regression?

  SSE, SSR, SST

  R-squared

  Errors (ε vs. e) - YouTube](https://www.youtube.com/watch?v=aq8VU5KLmkY)

  • for SSE, SSR and SST

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