LIN-31

OLS slope (2 pt)

Two-point slope.

Reading speed

GoverningOLS slope (2 pt)

Governing equation

m=(y_2-y_1)/(x_2-x_1)

where

x1: x1 (—)
y1: y1 (—)
x2: x2 (—)
y2: y2 (—)
m: OLS slope (2 pt) (—)

Lecture brief

Historical brief

Determinants, eigenvalues, least squares and Cayley–Hamilton are the nineteenth-century matrix craft behind every coupled system. The sheets invert, project and diagonalise small n. This sheet (LIN-31 — OLS slope (2 pt)) is the form associated with OLS slope (2 pt). Working symbols: $x1$ , $y1$ , $x2$ , $y2$ $\rightarrow$ $m$ . Two-point slope. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

m

from

x1

y1

x2

y2

in Linear algebra via

m=(y_2-y_1)/(x_2-x_1)

Two-point slope. Use it when a real linear algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

x1 = 0.000\,\mathrm{—}

y1 = 1.000\,\mathrm{—}

x2 = 2.000\,\mathrm{—}

y2 = 5.000\,\mathrm{—}

, the governing relation

m=(y_2-y_1)/(x_2-x_1)

yields

m = 2.000\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

x1 x10 —y1 y11 —x2 x22 —y2 y25 —

Outputs

OLS slope (2 pt) m2.000 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Two-point slope. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube