Linear Regression

Updated 04 Oct 2026

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What it is
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  models a response as a linear combination of coefficients and supplid features
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Formula
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  Simple: $\hat y=\beta_0+\beta_1x$ .
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  Multiple: $\hat y=\beta_0+\sum_{j=1}^{p}\beta_jx_j$ .
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  “Linear” refers to the coefficients; a feature can itself be a transformation such as $x^2$ .
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Fitting
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  ordinary Unavailable reference minimizes $\sum_i(y_i-\hat y_i)^2$ .
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Checked example
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  for $x=(1,2,3,4,5)$ and $y=(2,3,5,6,8)$ , the fitted line is $\hat y=0.3+1.5x$ .
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  at $x=6$ , the prediction is $9.3$ ; the training sum of squared errors is $0.3$ .
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Source correction
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  The regression deck’s displayed coefficients $15$ and $3$ , and prediction $93$ , disagree with its data and chart equation.
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  The spreadsheet function is INTERCEPT(known_y, known_x), not INTERSECT.
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  Forecast syntax distinguishes the query from training data: FORECAST.LINEAR(new_x, known_y, known_x).
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Reference
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  https://support.microsoft.com/en-us/excel/functions/intercept-function

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