Specifically, we see from model selection that it may be desirable to select only a subset from available predictors. Suppose that we apply linear regression to a data set, in which we have n observations and p predictors. In fact, when the number of predictors p increases, the resulting linear function will fit the data better and better. N

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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2 Specifically, we see from model selection that it may be desirable to select only a subset from available predictors. Suppose that we apply linear regression to a data set, in which we have n observations and p predictors. In fact, when the number of predictors p increases, the resulting linear function will fit the data better and better. Now consider an extreme case: When p = (n – 1), the linear function will fit all the n observations exactly (with probably the exception of a special math case). Without going to details of math, using 2 or 3 sentences, explain why we can fit all the n observations exactly with (n – 1) predictors.
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