correlation and causation
DESCRIPTION
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
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Correlation and CausationPart II – Correlation Coefficient
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This video is designed to accompany
pages 19-24in
Making Sense of UncertaintyActivities for Teaching Statistical
ReasoningVan-Griner Publishing Company
![Page 3: Correlation and Causation](https://reader035.vdocuments.us/reader035/viewer/2022062501/56815ef7550346895dcdb5e2/html5/thumbnails/3.jpg)
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?
![Page 4: Correlation and Causation](https://reader035.vdocuments.us/reader035/viewer/2022062501/56815ef7550346895dcdb5e2/html5/thumbnails/4.jpg)
Formula for “r”
The Correlation Coefficient is “r” measures the strength of the linear relationship between two variables “x” and “y”.
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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.
![Page 6: Correlation and Causation](https://reader035.vdocuments.us/reader035/viewer/2022062501/56815ef7550346895dcdb5e2/html5/thumbnails/6.jpg)
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?
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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
![Page 8: Correlation and Causation](https://reader035.vdocuments.us/reader035/viewer/2022062501/56815ef7550346895dcdb5e2/html5/thumbnails/8.jpg)
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!
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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.