Q u antif y ing the strength of bi v ariate relationships C OR R E - - PowerPoint PPT Presentation

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Q u antif y ing the strength of bi v ariate relationships C OR R E - - PowerPoint PPT Presentation

Mar 20, 2024 50 likes •513 views

Q u antif y ing the strength of bi v ariate relationships C OR R E L ATION AN D R E G R E SSION IN R Ben Ba u mer Assistant Professor at Smith College Correlation Correlation coe cient bet w een -1 and 1 Sign > direction Magnit u

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Quantifying the strength of bivariate relationships

C OR R E L ATION AN D R E G R E SSION IN R

Ben Baumer

Assistant Professor at Smith College

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CORRELATION AND REGRESSION IN R

Correlation

Correlation coecient between -1 and 1 Sign —> direction Magnitude —> strength

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CORRELATION AND REGRESSION IN R

Near perfect correlation

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CORRELATION AND REGRESSION IN R

Strong

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CORRELATION AND REGRESSION IN R

Moderate

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CORRELATION AND REGRESSION IN R

Weak

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CORRELATION AND REGRESSION IN R

Zero

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CORRELATION AND REGRESSION IN R

Negative

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CORRELATION AND REGRESSION IN R

Non-linear

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CORRELATION AND REGRESSION IN R

Non-linear correlation

run10 %>% filter(divPlace <= 10) %>% ggplot(aes(x = age, y = pace, color = gender)) + geom_point()

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CORRELATION AND REGRESSION IN R

Pearson product-moment correlation

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CORRELATION AND REGRESSION IN R

Pearson product-moment correlation

r(x,y) = √ (x − ) ⋅ (y − ) ∑i=1

n i

x ¯ 2 ∑i=1

n i

y ¯ 2 x − y − ∑i=1

n

( i x ¯) ( i y ¯)

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Let's practice!

C OR R E L ATION AN D R E G R E SSION IN R

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The Anscombe dataset

C OR R E L ATION AN D R E G R E SSION IN R

Ben Baumer

Assistant Professor at Smith College

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CORRELATION AND REGRESSION IN R

Anscombe

ggplot(data = Anscombe, aes(x = x, y = y)) + geom_point() + facet_wrap(~ set)

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CORRELATION AND REGRESSION IN R

Anscombe 1

Anscombe %>% filter(set == 1) %>% ggplot(aes(x = x, y = y)) + geom_point()

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CORRELATION AND REGRESSION IN R

Anscombe 2

Anscombe %>% filter(set == 2) %>% ggplot(aes(x = x, y = y)) + geom_point()

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CORRELATION AND REGRESSION IN R

Anscombe 3

Anscombe %>% filter(set == 3) %>% ggplot(aes(x = x, y = y)) + geom_point()

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CORRELATION AND REGRESSION IN R

Anscombe 4

Anscombe %>% filter(set == 4) %>% ggplot(aes(x = x, y = y)) + geom_point()

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Let's practice!

C OR R E L ATION AN D R E G R E SSION IN R

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Interpretation of Correlation

C OR R E L ATION AN D R E G R E SSION IN R

Ben Baumer

Assistant Professor at Smith College

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

Source: hp://well.blogs.nytimes.com/2015/12/02/the-close-ties-between- exercise-and-beer/

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CORRELATION AND REGRESSION IN R

Exercise and beer

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CORRELATION AND REGRESSION IN R

Exercise and beer

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CORRELATION AND REGRESSION IN R

Exercise and beer

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CORRELATION AND REGRESSION IN R

Exercise and beer

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CORRELATION AND REGRESSION IN R

NFL arrests

Source: hps://www.nytimes.com/2014/09/13/upshot/what-the-numbers- show-about-n-player-arrests.html

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CORRELATION AND REGRESSION IN R

NFL arrests

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CORRELATION AND REGRESSION IN R

NFL arrests

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CORRELATION AND REGRESSION IN R

NFL arrests

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CORRELATION AND REGRESSION IN R

Correlation vs. regression

Source: hp://www.nytimes.com/2012/11/02/business/questions-raised-on- withdrawal-of-congressional-research-services-report-on-tax-rates.html

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CORRELATION AND REGRESSION IN R

Correlation vs. regression

Source: hp://www.nytimes.com/2012/11/02/business/questions-raised-on- withdrawal-of-congressional-research-services-report-on-tax-rates.html

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CORRELATION AND REGRESSION IN R

Correlation vs. regression

Source: hp://www.nytimes.com/2012/11/02/business/questions-raised-on- withdrawal-of-congressional-research-services-report-on-tax-rates.html

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CORRELATION AND REGRESSION IN R

Can you plot a correlation?

Source: hp://heatst.com/world/no-correlation-between-voting-for-brexit- and-racism-study-nds/

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Let's practice!

C OR R E L ATION AN D R E G R E SSION IN R

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Spurious correlations

C OR R E L ATION AN D R E G R E SSION IN R

Ben Baumer

Assistant Professor at Smith College

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CORRELATION AND REGRESSION IN R

Spurious over time

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CORRELATION AND REGRESSION IN R

Spurious over time

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CORRELATION AND REGRESSION IN R

Spurious over space

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CORRELATION AND REGRESSION IN R

Spurious for whatever reason

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Let's practice!

C OR R E L ATION AN D R E G R E SSION IN R