Simply input the arrays of independent and dependent data and call the linreg function to see the interxept and slope:
$x gets [1,2,3,4,5] /* independent data: array */ $y gets [1,2,1.3,3.75,2.25] /* dependent data: array */ linreg($x, $y)
You could also get just the slope with slope($x, $y) or just the intercept with intercept($x, $y).
You can use Palamedes matrix operations to do the calculation step-by-step to get extra information such as the OLS estimate for the variance in the error term...
/* Commands */ $x gets [1,2,3,4,5] /* independent data: array */ $y gets [1,2,1.3,3.75,2.25] /* dependent data: array */ n gets count $y /* n: sample size */ p gets 2 /* p: number of predictors */ ν gets n-p /* nu: degrees of freedom */ y gets [$y]^T /* n x 1 matrix */ ones gets n # 1 $X gets [ones, $x]^T /* design matrix: n x p matrix */ y; $X /* show what we have so far */ /* y = $X cross β */ /* Therefore $X^-1 cross y = $X^-1 cross $X cross β = β */ /* N.B. No need to construct a pseudo-inverse anymore: this is done automatically */ β gets $X^-1 cross y; β /* response coefficients: p x 1 matrix */ /* break out the slope and intercept then show them */ intercept gets β after 0 after 0; intercept slope gets β after 1 after 0; slope ŷ gets $X cross β; ŷ /* fitted values */ residuals gets ŷ - y; residuals /* residuals from the regression */ /* ss: OLS estimate for the variance in the error term */ ss gets ((residuals^T cross residuals) after 0 after 0)/ν; ss /* standard error of the regression (SER) AKA standard error of the equation (SEE) */ sqrt(ss) |
/* Results */ $x ← [1, 2, 3, 4, 5] $y ← [1, 2, 1.3, 3.75, 2.25] n ← count($y) p ← 2 ν ← n - p y ← [$y] ^ T ones ← n # 1 $X ← [ones, $x] ^ T y → [[ 1 ], ... [ 2 ], ... [ 1.3 ], ... [ 3.75 ], ... [ 2.25 ]] $X → [[ 1, 1 ], ... [ 1, 2 ], ... [ 1, 3 ], ... [ 1, 4 ], ... [ 1, 5 ]] β ← $X ^ -1 × y β → [[ 0.7849999999999997 ], ... [ 0.42500000000000027 ]] intercept ← β ∘ 0 ∘ 0 intercept → 0.7849999999999997 slope ← β ∘ 1 ∘ 0 slope → 0.42500000000000027 ŷ ← $X × β ŷ → [[ 1.21 ], ... [ 1.6350000000000002 ], ... [ 2.0600000000000005 ], ... [ 2.4850000000000008 ], ... [ 2.910000000000001 ]] residuals ← ŷ - y residuals → [[ 0.20999999999999996 ], ... [ -0.36499999999999977 ], ... [ 0.7600000000000005 ], ... [ -1.2649999999999992 ], ... [ 0.660000000000001 ]] ss ← ((residuals ^ T × residuals) ∘ 0 ∘ 0) / ν ss → 0.9302499999999999 sqrt(ss) → 0.9644946863513556 |
Last update: Fri Sep 23 2016