correlation and causation
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Correlation and Causation. Part II – Correlation Coefficient. This video is designed to accompany pages 19-24 in Making Sense of Uncertainty Activities for Teaching Statistical Reasoning Van- Griner Publishing Company. Defining a Need. - PowerPoint PPT PresentationTRANSCRIPT
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.