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

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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