Correlation and CausationPart II – Correlation Coefficient

This video is designed to accompany

pages 19-24

in

Making Sense of UncertaintyActivities for Teaching Statistical

ReasoningVan-Griner Publishing Company

Defining a Need

The Correlation Coefficient is simply a numerical way of summarizing the relationship you’d see between two variables that you could represent with a scatterplot.

Positive association.How strong is it?

Formula for “r”

The Correlation Coefficient is “r” measures the strength of the linear relationship between two variables “x” and “y”.

Before we compute it …

1. It is only appropriate to compute r if the scatterplot of y versus x exhibits a linear trend

2. r will always be between -1 and 1. 3. r will be negative if the points in the

scatterplot have a downward trend from left to right

4. r will be positive if the points in the scatterplot have an upward trend from left to right

5. The closer r is to 1 in absolute value the tighter the cluster of points about the linear trend and the stronger the association between x and y

6. If r is close to 0 then the association is weak.

Simple Scatterplot

15 20 25 30 35 40 45 50 55 60 6550

60

70

80

90

100

110

Scatterplot

Age

Glu

cose L

Evels

Modera

te,

posi

tive

corr

ela

tion

?

Compute It!

Subject Age x

Glucose

Level y

xy x2 y2

1 43 99 4257 1849 98012 21 65 1365 441 42253 25 79 1975 625 62414 42 75 3150 1764 56255 57 87 4959 3249 75696 59 81 4779 3481 6561

ΣΣx = 247

Σy = 486

Σxy = 20485

Σx2 = 11409

Σy2 = 40022

Scatterplots Revisited

Time Spent Studying

Stu

den

t G

rad

es

r = 0

.75

Quiz Average

Fin

al Exam

S

core

r = 0.02

GNP per capita

Lif

e E

xp

ecta

ncy a

t B

irth

Not appropriate to

use r since plot is

curved

Hours Exercised

LD

L L

evels

r = -0.93

Got it!

One-Sentence Reflection

The correlation coefficient is the most common numerical measure of the strength of a straight line relationship between two variables that can represented by a scatterplot.