Think
The h ig h e st a ltitu d e is
5000 m. So a reasonable
scale on th e a ltitu d e axis
is 0 to 5500 w ith every
1000 m labeled. You can
use sim ilar reasoning to
label th e tem perature
axis.
Pr o b l em 1 Making a Scatter Plot and Describing Its Correlation
Temperature The table shows the altitude of an airplane and the temperature
outside the plane.Plane A ltitude and Outside Tem peratureAltitude (m) (^0500100015002000250030003500400045005000)
Temperature
(°F)
59.0 59.2 61.3 55.5 ;Y.-41.6.
'm J
29.8
L j
29.9 18.1 26.2 12.4 0,
0 Make a scatter plot of the data.
Treat th e d ata as ordered pairs. For th e altitude of
1500 m an d the tem p eratu re of 55.5°F, plot (1500, 55.5).
0 What type of relationship does the scatter plot show?
The tem p eratu re outside th e p lan e ten d s to decrease as
the altitude of th e plane increases. So th e data have a
negative correlation.
Go t I t? 1. a. Make a scatter plot of th e d ata in th e table
below. W hat type of relationship does the
scatter plot show?
Plane A ltitude and
Outside Temperature
60^ 9 •
40
m
|- 20
Ol
^
Altitude (m)
r i
Gasoline Purchases
Dollars Spent 10 11 9 1 0 13 5 8. 4
Gallons Bought 2.5 2.8 2 .3 2 .6 3.3 1.3 2.2 1.1
b. Reasoning C onsider th e p o p u latio n of a city an d th e n u m b e r of letters
in th e n a m e of th e city. W ould you expect a positive correlation, a
negative correlation, or no correlation b etw e en th e two sets of data?
Explain your reasoning.
W hen two sets of data have a positive or negative
correlation, you can u se a tre n d line to show the
correlation more clearly. A trend line is a line on
a scatter plot, draw n n e a r th e points, th a t shows
a correlation.
You can u se a tren d line to estim ate a value betw een
two know n d ata values or to p re d ic t a value outside th e range of know n d ata values.
Interpolation is estim ating a value b etw een two know n values. Extrapolation is
predicting a value o utside th e range of know n values.
c
PowerAlgebra.com J Lesso n 5- 7 Scat t er Pl o t s an d Tr en d Li n es^337