3.3 power point

8/7/2019 3.3 Power Point

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Correlation andCorrelation and

Regression Wisdom:Regression Wisdom:Section 3.3Section 3.3


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CautionsCautions

Correlation and regression describe onlyCorrelation and regression describe onlylinear relationships!linear relationships! You can do theYou can do thecalculations for any relationship betweencalculations for any relationship between

two variables, but the results are useful onlytwo variables, but the results are useful onlyif the scatterplot shows a linear pattern.if the scatterplot shows a linear pattern.

Extrapolation often produces unreliableExtrapolation often produces unreliable

results!results! Correlation is not resistant!Correlation is not resistant! Always plotAlways plot

your data and look for unusual observationsyour data and look for unusual observationsbefore you interpret correlation.before you interpret correlation.


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Which Points Have theWhich Points Have the

Influence?Influence? Each point has an influence on the LSR line,Each point has an influence on the LSR line,

some make large contributions and somesome make large contributions and some

small. Some make positive contributions andsmall. Some make positive contributions andsome negative.some negative.

Our goal is to learn to recognize the points theOur goal is to learn to recognize the points the

points in a data set that may have an unusuallypoints in a data set that may have an unusuallylarge influence on where the regression linelarge influence on where the regression line

goes or on the size and sign or the correlation.goes or on the size and sign or the correlation.


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Outliers and InfluentialOutliers and Influential

Observations in RegressionObservations in Regression


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0

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0 5 10 15 20 25 30 35 40 45

Aver e_Life_Span

Coll ction1 Sc tt r Plot

Animal LongevityAnimal Longevity

TheThe

relationrelation--shipship

betweenbetween

maximummaximum

andandaverageaverage

life spanlife span

forfor

mammals.mammals.

Beaver: avg. = 5

max = 50

Elephant: avg. = 35

max = 70

Hippo: avg. = 41

max = 54


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If you look at the entire sample, the beaver,If you look at the entire sample, the beaver,

elephant, and hippo are the oddballs of theelephant, and hippo are the oddballs of the

bunch.bunch.

The LSR line for all the mammals in theThe LSR line for all the mammals in the

sample is:sample is:

where is the predicted maximumwhere is the predicted maximum

longevity andlongevity and AA stands for observedstands for observed

average longevity.average longevity.

The correlation for the relationship is .77.The correlation for the relationship is .77.

AM 58.153.10 !

M


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Are Outliers Always Influential?Are Outliers Always Influential?

In Chapter 1, outliers were influentialIn Chapter 1, outliers were influentialpoints, because they were far from thepoints, because they were far from the

other values AND the mean changesother values AND the mean changesdrastically when they are removed. Indrastically when they are removed. Inregression, not all outliers are influential.regression, not all outliers are influential.Influential points often have smallInfluential points often have small

residuals because they pull theresiduals because they pull theregression line toward themselves, soregression line toward themselves, sojust looking at a residual plot is notjust looking at a residual plot is notenough.enough.


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How Do We Know?How Do We Know?

The surest way to verify that a point isThe surest way to verify that a point is

influential is to find the regression lineinfluential is to find the regression line

both with and without the suspect point. Ifboth with and without the suspect point. Ifthe line moves more than a small amountthe line moves more than a small amount

when the point is deleted, the point iswhen the point is deleted, the point is

influential.influential.


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Maxi _ i _ an = 1.58Average_ i e_ an + 10.5; r2 = 0.59

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Av r g if

Collection 1 Scatter Plot

With all mammals:slope = 1.58

and r = .77

Maximum_ i e_Span = 1.96Average_ i e_Span + 6.3; r2 = 0.64

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Av r g if


Without hippos:slope = 1.96

and r = .80

Maximum_ i e_Span = 1.53Average_ i e_Span + 11; r2 = 0.52

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Av r g if


Without elephant:slope = 1.53

and r = .72

Maximum_ i e_Span = 1.69Average_ i e_Span + 8.1; r2 = 0.69

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Av r g if


Without beaver:slope = 1.69

and r = .83


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The Anscombe sets:The Anscombe sets: M

ake a scatterplot, find the LSR equation,M

ake a scatterplot, find the LSR equation,and find the correlation:and find the correlation:

Set 1:Set 1: xx yy

1010 8.048.04

88 6.956.95

1313 7.587.5899 8.818.81

1111 8.338.33

1414 9.969.96

66 7.247.2444 4.264.26

12 10.8412 10.84

77 4.824.82

55 5.685.68

xy 5.!

r = .82


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Make a scatterplot, find the LSR equation,M


Set 2:Set 2: xx yy

1010 9.149.14

88 8.148.14

1313 8.748.7499 8.778.77

1111 9.269.26

1414 8.108.10

66 6.136.1344 3.103.10

12 9.1312 9.13

77 7.267.26

55 4.744.74

The Anscombe sets:The Anscombe sets:

xy 5.!

r = .82


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Set 3:Set 3: xx yy

1010 7.467.46

88 6.776.77

13 12.7413 12.7499 7.117.11

1111 7.817.81

1414 8.848.84

66 6.086.0844 5.395.39

12 8.1512 8.15

77 6.426.42

55 5.735.73


xy 5.!

r = .82


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Set 4:Set 4: xx yy

88 6.956.95

88 5.765.76

88 7.717.7188 8.848.84

88 8.478.47

88 7.047.04

88 5.255.2519 12.5019 12.50

8 5.568 5.56

88 7.917.91

88 6.896.89


xy 5.!

r = .82


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QuestionsQuestions

Which plots have a point influential withWhich plots have a point influential with

respect to the slope of the LSR line? Howrespect to the slope of the LSR line? How

would the slope change if the point waswould the slope change if the point was

removed?removed?

Which plots have a that is influential withWhich plots have a that is influential with

respect to the correlation? How would therespect to the correlation? How would the

correlation change if the point wascorrelation change if the point wasremoved?removed?


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Matching:Matching:


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Beware the Lurking Variable!Beware the Lurking Variable!


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Imported Goods and Spending on HealthImported Goods and Spending on Health

The explanatory variable isThe explanatory variable is

the dollar value of goodsthe dollar value of goodsimported into the USimported into the US

between 1990 and 2001.between 1990 and 2001.

The response variable isThe response variable is

private spending on healthprivate spending on healthin these years.in these years.


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Are You in a Relationship?Are You in a Relationship?

There is no economic relationshipThere is no economic relationshipbetween these variables. The strongbetween these variables. The strong

association is due entirely to the fact thatassociation is due entirely to the fact thatboth imports and health spending grewboth imports and health spending grewrapidly in these years. The common yearrapidly in these years. The common yearfor each point is a lurking variable. Anyfor each point is a lurking variable. Any

two variables that both increase overtwo variables that both increase overtime will show a strong association. Thistime will show a strong association. Thisdoes not mean that one variable explainsdoes not mean that one variable explainsor influences each other.or influences each other.


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Hey, Watch it!Hey, Watch it!

Association doesAssociation does notnot

imply causation!!!imply causation!!!

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