Visualization of Linear Models Correlation and Regression Possums - - PowerPoint PPT Presentation

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Visualization of Linear Models Correlation and Regression Possums - - PowerPoint PPT Presentation

Jul 11, 2023 165 likes •408 views

CORRELATION AND REGRESSION Visualization of Linear Models Correlation and Regression Possums > ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() Correlation and Regression Through the origin > ggplot(data = possum,

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CORRELATION AND REGRESSION

Visualization of Linear Models

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Correlation and Regression

Possums

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

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Correlation and Regression

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

Through the origin, beer 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

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

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

Ignore standard errors

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

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CORRELATION AND REGRESSION

Let’s practice!

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CORRELATION AND REGRESSION

Understanding the linear model

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Correlation and Regression

Generic statistical model

response = f(explanatory) + noise

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Correlation and Regression

Generic linear model

response = intercept + (slope * explanatory) + noise

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Correlation and Regression

Regression model

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Correlation and Regression

Fied values

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Correlation and Regression

Residuals

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Correlation and Regression

Fiing procedure

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Correlation and Regression

Least squares

  • Easy, deterministic, unique solution
  • Residuals sum to zero
  • Line must pass through
  • Other criteria exist—just not in this course
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Correlation and Regression

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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CORRELATION AND REGRESSION

Let’s practice!

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CORRELATION AND REGRESSION

Regression vs. regression to the mean

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Correlation and Regression

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

Galton's data

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Correlation and Regression

Regression modeling

  • "Regression": techniques for modeling a quantitative response
  • Types of regression models:
  • Least squares
  • Weighted
  • Generalized
  • Nonparametric
  • Ridge
  • Bayesian
  • …
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CORRELATION AND REGRESSION

Let’s practice!