Q: When P(# Regressors)=N(# Observations), does R^2 = 1?

Question

I'm challenging a question from a quiz in a Data Science curriculum. The answer I gave was "Not enough information." The tester claims the answer is "R^2 = 1." I can't make sense of this mathematically or conceptually. I ran a regression with SciKit learn to test it, and did not receive R^2 = 1.

The question: If P = N, R-Squared of the sample will be: ? Where, P: Number of regressors N: Number of observations in a sample

I appreciate any input you can volunteer before I raise a bit of hell. :)

Answer 1

The number of regressor is non sense, but number of predicting variables.

In that case indeed R² is 1.

Pretty nice debate here (it is indeed a stackexchange topic you've got) : https://stats.stackexchange.com/questions/65192/how-can-i-get-an-r-squared-value-of-1-fit-100