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

Jul 11, 2023 •165 likes •406 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,

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, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 2.5)
Correlation and Regression Through the origin, be � er fit > ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 1.7)
Correlation and Regression Not through the origin > ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 40, slope = 1.3)
Correlation and Regression The "best" fit line > ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm")
Correlation and Regression Ignore standard errors > ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm", se = FALSE)
CORRELATION AND REGRESSION Let’s practice!
CORRELATION AND REGRESSION Understanding the linear model
Correlation and Regression Generic statistical model response = f(explanatory) + noise
Correlation and Regression Generic linear model response = intercept + (slope * explanatory) + noise
Correlation and Regression Regression model
Correlation and Regression Fi � ed values
Correlation and Regression Residuals
Correlation and Regression Fi � ing procedure
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
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—be � er: noise
CORRELATION AND REGRESSION Let’s practice!
CORRELATION AND REGRESSION Regression vs. regression to the mean
Correlation and Regression Heredity ● Galton's "regression to the mean" ● Thought experiment: consider the heights of the children of NBA players
Correlation and Regression Galton's data
Correlation and Regression Regression modeling ● "Regression": techniques for modeling a quantitative response ● Types of regression models: ● Least squares ● Weighted ● Generalized ● Nonparametric ● Ridge ● Bayesian ● …
CORRELATION AND REGRESSION Let’s practice!

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