Correlation and Regression
1
Prerequisites
2
Visualizing two variables
2.1
Scatterplots
Exercise
2.2
Boxplots as discretized/conditioned scatterplots
Exercise
2.3
Creating scatterplots
Exercise
Characterizing scatterplots
2.4
Transformations
Exercise
2.5
Identifying outliers
Exercise
3
Correlation
Understanding correlation scale
Understanding correlation sign
3.1
Computing correlation
Exercise
3.2
Exploring Anscombe
Exercise
Perception of correlation
Perception of correlation (2)
Exercise
Interpreting correlation in context
Correlation and causation
3.3
Spurious correlation in random data
4
Simple linear regression
4.1
The “best fit” line
Exercise
4.2
Uniqueness of least squares regression line
Regression model terminology
4.2.1
Regression model output terminology
4.3
Fitting a linear model “by hand”
4.4
Regression to the mean
Exercise
“Regression” in the parlance of our time
5
Interpreting regression models
Interpretation of coefficients
Interpretation in context
5.1
Fitting simple linear models
Exercise
Units and scale
5.2
The lm summary output
Exercise
5.3
Fitted values and residuals
Exercise
5.4
Tidying your linear model
Exercise
5.5
Making predictions
Exercise
5.6
Adding a regression line to a plot manually
Exercise
6
Model Fit
RMSE
6.1
Standard error of residuals
Exercise
6.2
Assessing simple linear model fit
Interpretation of
\(R^2\)
6.3
Linear vs. average
Exercise
6.4
Leverage
Exercise
6.5
Influence
6.6
Removing outliers
6.7
High leverage points
References
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Correlation and Regression
References