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LIN-31

OLS slope (2 pt)

Two-point slope.

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GoverningOLS slope (2 pt)

Governing equation

m=(y2−y1)/(x2−x1)m=(y_2-y_1)/(x_2-x_1)

x2∈[−10,10]x2 \in \left[-10, 10\right]

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

LIN-31 · curve
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①

Governing law — red

m=(y2−y1)/(x2−x1)m=(y_2-y_1)/(x_2-x_1)

x2∈[−10,10]x2 \in \left[-10, 10\right]

x2=−10x2 = -10m=4×109m = 4\times 10^{9}

②

Domain of the variable — blue

x2min⁡=−10,x2max⁡=10x2_{\min} = -10,\quad x2_{\max} = 10

x2∈[−10,10]x2 \in \left[-10, 10\right]

x2=−10x2 = -10x2=−10x2 = -10

③

Response curve — green

m=(y2−y1)/(x2−x1)m=(y_2-y_1)/(x_2-x_1)

x2∈[−10,10]x2 \in \left[-10, 10\right]

x2=−10x2 = -10m=4×109m = 4\times 10^{9}

④

Rate of change — amber

dmdx2\frac{\mathrm{d}m}{\mathrm{d}x2}

x2∈[−10,10]x2 \in \left[-10, 10\right]

x2=−9.874x2 = -9.874m′=0m^{\prime} = 0

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: x1x1, y1y1, x2x2, y2y2 →\rightarrow mm. Two-point slope. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute mm from x1x1, y1y1, x2x2, y2y2 in Linear algebra via m=(y2−y1)/(x2−x1)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 —x1 = 0.000\,\mathrm{—}, y1=1.000 —y1 = 1.000\,\mathrm{—}, x2=2.000 —x2 = 2.000\,\mathrm{—}, y2=5.000 —y2 = 5.000\,\mathrm{—}, the governing relation m=(y2−y1)/(x2−x1)m=(y_2-y_1)/(x_2-x_1) yields m=2.000 —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.

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Inputs

Outputs

  • OLS slope (2 pt) m2.000 —
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LIN-31 · curve
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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