Vis u ali z ation of Linear Models C OR R E L ATION AN D R E G R - - PowerPoint PPT Presentation

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Feb 29, 2024 203 likes •440 views

Vis u ali z ation of Linear Models 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 Poss u ms ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() CORRELATION AND REGRESSION IN R Thro

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Visualization of Linear Models

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

Possums

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point()

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CORRELATION AND REGRESSION IN R

Through the origin

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 2.5)

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CORRELATION AND REGRESSION IN R

Through the origin, better fit

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 1.7)

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CORRELATION AND REGRESSION IN R

Not through the origin

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 40, slope = 1.3)

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CORRELATION AND REGRESSION IN R

The "best" fit line

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm")

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CORRELATION AND REGRESSION IN R

Ignore standard errors

ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm", se = FALSE)

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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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Understanding Linear Models

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

Generic statistical model

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CORRELATION AND REGRESSION IN R

Generic linear model

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CORRELATION AND REGRESSION IN R

Regression model

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CORRELATION AND REGRESSION IN R

Fitted values

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CORRELATION AND REGRESSION IN R

Residuals

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CORRELATION AND REGRESSION IN R

Fitting procedure

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CORRELATION AND REGRESSION IN R

Least squares

Easy, deterministic, unique solution Residuals sum to zero Line must pass through ( , ) Other criteria exist—just not in this course

x ¯ y ¯

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CORRELATION AND REGRESSION IN R

Key concepts

Y-hat is expected value given corresponding X Beta-hats are estimates of true, unknown betas Residuals (e's) are estimates of true, unknown epsilons "Error" may be misleading term—beer: noise

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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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Regression vs. regression to the mean

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

Heredity

Galton's "regression to the mean" Thought experiment: consider the heights of the children of NBA players

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CORRELATION AND REGRESSION IN R

Galton's data

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CORRELATION AND REGRESSION IN R

Regression modeling

"Regression": techniques for modeling a quantitative response Types of regression models: Least squares Weighted Generalized Nonparametric Ridge Bayesian . . .

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Let's practice!

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