query: How can one show mathematically that adding many variables will only increase R-squared?
positive_passages.docid: 155420
positive_passages.text: Why does adding more terms into a linear model always increase the r-squared value?
negative_passages.docid: 15030
negative_passages.text: Is there a law that you can add or multiply to both sides of an equation?
negative_passages.docid: 132484
negative_passages.text: Not so easy optimization of variables?
negative_passages.docid: 132470
negative_passages.text: Does $\mathbb R^2$ contain more numbers than $\mathbb R^1$?
negative_passages.docid: 19279
negative_passages.text: dropping injectivity from multivariable change of variables
negative_passages.docid: 1707
negative_passages.text: How does one prove that addition on $\mathbb{R}$ is associative?
negative_passages.docid: 2050
negative_passages.text: Multivariable Taylor expansion does not work as expected
negative_passages.docid: 77384
negative_passages.text: How to test for a monotonic relationship between two variables, without assuming a specific functional model?
negative_passages.docid: 153028
negative_passages.text: Showing that the product of vector magnitudes is larger than their dot product
negative_passages.docid: 84228
negative_passages.text: What's the best way make an "augmented" coefficient matrix?
negative_passages.docid: 91668
negative_passages.text: Sign of Estimate (Coefficient) of Interaction Terms
negative_passages.docid: 81757
negative_passages.text: How to include a linear and quadratic term when also including interaction with those variables?
negative_passages.docid: 157122
negative_passages.text: How can factor-levels be automatically chosen in R to maximize the number of positive coefficients in a regression model?
negative_passages.docid: 9414
negative_passages.text: Is There a Natural Way to Extend Repeated Exponentiation Beyond Integers?
negative_passages.docid: 122957
negative_passages.text: Intuitive proof of multivariable changing of variables formula (jacobian) without using mapping and/or measure theory?
negative_passages.docid: 47432
negative_passages.text: Change of Variables in Limits (Part 1)
negative_passages.docid: 6402
negative_passages.text: What does negative R-squared mean?