correlation and causation

Correlation and CausationPart II – Correlation Coefficient

This video is designed to accompany

pages 19-24in

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

LEv

els

Mod

erat

e, p

ositi

ve

corre

latio

n?

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 6561Σ Σx =

247Σy = 486

Σxy = 20485

Σx2 = 11409 Σy2 = 40022

Scatterplots Revisited

Time Spent Studying

Stud

ent

Gra

des

r = 0.75

Quiz Average

Fina

l Exa

m

Scor

e

r = 0.02GNP per capita

Life

Exp

ecta

ncy

at

Birt

h

Not appropriate to

use r since plot is

curved

Hours Exercised

LDL

Leve

ls

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.