All courses Math I · S-ID.6.c 56 of 59
Fit a linear function to data when a scatter plot suggests a linear association.

Decide whether a scatter plot suggests a linear association

Problem
Does this scatter-plot description suggest a linear association: points fall close to an upward sloping straight band?
Your answer
Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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Hint

Look for whether the points follow an approximate straight line rather than a curve or random cloud.

An upward sloping straight band suggests a positive linear association.

Solution walkthrough

01

Check the form

\[\text{points}~\text{stay}~\text{close}~\text{to}~a~\text{straight}~\text{band}\]

An approximate straight band, rather than a curve, supports linear form.

02

Check the direction

\[\text{the}~\text{band}~\text{slopes}~\text{upward}~\text{from}~\text{left}~\text{to}~\text{right}\]

As x increases, y tends to increase, so the direction is positive.

03

Combine form and direction

\[\text{straight}~+~\text{upward}=\text{positive}~\text{linear}~\text{association}\]

Scatter around the band is expected and does not require every point to lie exactly on a line.

04

State the decision

\[\text{Yes},~\text{the}~\text{points}~\text{stay}~\text{close}~\text{to}~\text{an}~\text{upward}-\text{sloping}~\text{straight}~\text{band},~\text{so}~\text{the}~\text{association}~\text{is}~\text{positive}~\text{and}~\text{linear}.\]

The description supports a positive linear association.

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Another way

  1. Imagine one trend line through the middle of the points; a rising straight line fits the described band.

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Common mistake

Do not use increasing alone as proof of linearity; the decisive form clue is the approximately straight band.