Are these Two-variable Data notes free?

Yes. The full 3-page Two-variable Data sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Two-variable Data revision sheet cover?

What a scatterplot and its model are, Reading a straight model, the model, always in this form, m, the change in y for one more unit of x, b, the value the model gives at x=0, how far one observation sits off the model, Which way does the cloud lean, Positive association, Negative association, Worked: what m and b mean, Worked: how far off the model an observation sits, Linear or exponential, decided from a table.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Two-variable Data — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Two-variable Data, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Two-variable Data revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Two-variable Data in one look

a cloud of observations, and the line or curve drawn through the middle of it

What a scatterplot and its model are

each dot is one observation with two measurements, one read off each axis. The plot shows individuals, not totals
a MODEL is the line or curve drawn to summarise the cloud, so almost no dot sits exactly on it. The line of best fit is the straight one that comes closest to the whole cloud at once, with roughly half the dots above it and half below
the direction of the cloud is its association: rising left to right is positive, falling is negative, and no straight tilt at all means no linear association to describe

Reading a straight model

the model, always in this form y=mx+b
m, the change in y for one more unit of x m=y_2-y_1/x_2-x_1
b, the value the model gives at x=0 b=y-mx
how far one observation sits off the model residual=actual-predicted

Which way does the cloud lean

Positive association

as x increases, y tends to increase as well
the slope m of the line of best fit is POSITIVE
the dots still scatter about the line, they never sit on it

Negative association

as x increases, y tends to decrease
the slope m of the line of best fit is NEGATIVE
a falling line is still a good model, it is not a worse one

Worked: what m and b mean

Q. a club's membership x weeks after it opened is modelled by y=2.4x+18. What do 2.4 and 18 each stand for, and what does the model predict at week 25?

b first: put x=0 into the model, which gives y=18, the membership when the club opened
m next: every extra week adds 2.4 to y, so the club gains about 2.4 members a week
predict at x=25: 2.4×25=60, then 60+18=78

Answer: 18 is the starting membership, 2.4 is the weekly gain, and the model predicts 78 members at week 25

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Two-variable Data sheet covers

What a scatterplot and its model are
Reading a straight model
the model, always in this form
m, the change in y for one more unit of x
b, the value the model gives at x=0
how far one observation sits off the model
Which way does the cloud lean
Positive association
Negative association
Worked: what m and b mean
Worked: how far off the model an observation sits
Linear or exponential, decided from a table
Association is not cause
Two growth shapes, side by side
Pacing, the calculator, and the adaptive second module
Traps that cost points
Tricks that save time

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