![]() Let’s write down a simple formula which represents a line where some outcome \(z\) is related to a variable \(x\): We just learned how to represent a line, i.e. with two numbers called intercept and slope. However, the line seems at too high a level - the point at which it crosses the y-axis is called the intercept and it’s too high. ![]() Clearly, a better line would be not be flat, but have a slope, i.e. go upwards: Now that doesn’t seem a particularly good way to summarize the relationship. Plot(dist ~ speed, data = cars, xlab = "Speed (in Miles Per Hour)", ylab = "Stopping Distance (in Feet)", main = "Stopping Distance vs Speed", pch = 20, cex = 2, col = "red") abline( a = 60, b = 0, lw= 3) 12.1 Crime Rate vs Probability of Arrest.10.1 John Snow and the London Cholera Epidemic.7.3 Randomized Control Trials (RCT) Primer.6.6 The Classical Regression Model (CRM).6.5 What is true? What are Statistical Models?.6.4 Uncertainty in Regression Estimates.6.2 Taking Eleven Samples From The Population.5.5 (Unobserved) Individual Heterogeneity.3.9 A Particular Rescaling: The \(\log\) Transform.3.4 Correlation, Covariance and Linearity.3.2 Ordinary Least Squares (OLS) Estimator. ![]()
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