Algebra 1 Common Core Student Edition, Grade 8-9

Scatter Plots

and Trend Lines

Common Core State Standards

S-ID.B.6c Fit a linear function for a scatter plot that

suggests a linear association. Also S-ID.B.6a, S-ID.C.7,

S-ID.C.8, S-ID.C.9

MP 1, MP 2, M P 3 , M P 4

Objectives To write an eq u a tio n of a tren d line an d of a line of best fit

To use a tren d line an d a line of best fit to m ake predictions

Would you expect

th e number o f

albums downloaded

to have an e ffe c t

on CD sales?

MATHEMAIICAL

PRACTICES

Getting Ready!

The table shows the number of digital

albums downloaded per y e a r and th e number

of CDs sold by manufacturers per year.

What relationship exists between the two

sets o f data? Predict the number of CDs

sold and th e num ber o f albums downloaded

in 2010. E x p l a i n y o u r r e a s o n i n g. S9

Music Sales

Albums

Downloaded

(m illio ns) I

CDs Sold

(m illio ns)

Source: Recording Industry Association of America

Lesson

Vocabulary

scat t er p l o t

• positive
  co r r elat io n


• negat ive
  co r r elat io n


• no correlat ion


• trend line


• interpolation


• extrapolation


• line of best fit


• correlation
  coef f icient


• causation

In the Solve It, th e n u m b e r of album s dow nloaded p er y ear an d th e n u m b e r of CDs sold

p e r y ear are related.

Esse n t i a l U n d e r st a n d i n g You can d eterm in e w h e th e r two sets of num erical

d ata are related by graphing th e m as ordered pairs. If th e two sets of d ata are related,

you m ay be able to use a line to estim ate or predict values.

A scatter plot is a graph th at relates two different sets of d ata by displaying them

as ordered pairs. Most scatter plots are in th e first q u a d ra n t of th e coordinate plane

because th e data are usually positive num bers.

You can use scatter plots to find tren d s in data. The scatter plots below show th e three

types of relationships th a t two sets of d ata m ay have.

0

« «

e

0

• •

0

• •

When y ten d s to increase as x

increases, th e two sets of data

have a positive correlation.

When y ten d s to decrease as x

increases, th e two sets of data

have a negative correlation.

When x a n d y are n o t related,

th e two sets of d ata have

no correlation.

336 Chap t er 5 Linear Funct ions