Suppose you have $n+1$ data points $(x_1,y_1),\dots, (x_{n+1},y_{n+1})$ and want to fit a linear regression with a constant term and $n$ predictors to this data. Is the line a perfect fit? Explain your answer.
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Use your knowledge of linear equations and the number of points versus the number of predictors to analyze the fit. Remember, with 'n' predictors, you can perfectly fit 'n' data points if each point contributes independent information. Think about whether adding one more point to this system would still allow a perfect fit, and consider the cases when points are in a perfect linear arrangement versus when they are not.
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