Set up the design matrix for fitting y = β₀ + β₁x to points (2, 1), (5, 2), (7, 3).
Compare with the model answer
X = [[1, 2], [1, 5], [1, 7]], y = (1, 2, 3); solve XᵀXβ = Xᵀy.
Applications to Linear Models
Regression as least squares: the design matrix X, parameter vector β and observation vector y, the least-squares line y = β₀ + β₁x, residuals, and fitting other curves.
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parameter vector observation vector
Notes
Linear model y = Xβ + ε. Least-squares line: X has a column of 1s and a column of x values; solve XᵀXβ = Xᵀy.
Exam angle
Slide 2
Slide 3
In some applications, it is necessary to fit data points with something other than
Notes
Other curves (e.g. y = β₀ + β₁x + β₂x²) are still LINEAR in the parameters: add a column for x².
Example:
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