Algebra 1 Common Core Student Edition, Grade 8-9

Thi nl c
What does the value
of the correlation
coefficient mean?
The correlation
coefficient of 0.996
is close to 1. So th e re
is a stro n g p o sitive
correlation between the
academic year and the
cost of attending college.

The tren d line th at shows th e relationship betw een two sets of d ata m o st accurately is

called the line o f best fit. A graphing calculator co m p u tes th e eq u a tio n of th e line of

b est fit using a m e th o d called lin ear regression.

The graphing calculator also gives you the

correlation coefficient r, a n u m b e r from

• 1 to 1, th at tells you how closely the
  eq u a tio n m odels th e data.

I h e n e a re r r is to 1 or -1, th e m ore closely th e d ata cluster a ro u n d th e line of b est fit.

If r i s n e a r 1, th e d ata lie close to a line of b est fit w ith positive slope. If r i s n e a r — 1,

th e d ata lie close to a line of b est fit w ith negative slope.

Finding the Line of Best Fit

Co l l e g e Tu i t i o n Use a graphing calculator to find the equation

of the line of best fit for the data at the right. What is the

correlation coefficient to three decimal places? Predict the

cost of attending in the 2012-2013 academ ic year.

St e p 1 Press. From the ED I T menu, choose Ed i t. Enter

th e years into L t. Let x = 2000 rep resen t academ ic year

2000-2001, x = 2001 re p resen t 2001-2002, an d so on.

Enter the costs into L2.

St ep 2 Press Hi. C h o o s e L i n R e g ( a x + b) from th e CA LC

m enu. Press to find th e eq u a tio n of th e line of

best fit a n d th e correlation coefficient. The calculator

uses th e form y = ax + b for the equation.

Average Tuition and Fees

at Public 4-Year Colleges

iiip mm

2000-2001 3508

2001-2002 3766

2002-2003 4098

2003-2004 4645

2004-2005 5126

2005-2006 5492

2006-2007 5836

Source: The College Board

r= -1 r= 0 r = 1

I «......... -~-F~...— » I

strong negative no strong positive

correlation correlation correlation

R ound to th e n ea rest h u n d re d th. The eq u a tio n of th e line of best fit is

y = 409.43jc — 815,446.71. The correlation coefficient is a b o u t 0.996.

St e p 3 Predict th e cost of atten d in g in th e 2012-2013 academ ic year.

y = 409.43x - 815,446.71 Use t he eq uat i o n o f t he l i ne o f b est f i t.

y = 409.43(2012) - 815,446.71 Su b st i t u t e 2 0 1 2 for x.

y ~ 8326 Si m p l i f y. Ro u n d t o t h e n e a r e s t w h o l e n u m b e r.

The cost of atten d in g a four-year public college in th e 2012-2013 academ ic year is

predicted to be ab o u t $8326.

\

y-intercept

correlat ion

coefficient

nPowerAlgebra.com J Lesson 5-7 Scatter Plots and Trend Lines^339