4/17/2023

Summarizing Bivariate Data

• Scatterplots - Return to ClassDataS23.R

Common Types of Relationships

• No Association
• Positive Association
• Negative Association

Scatterplot Smoothing

• 1970 Draft Lottery Data

Measuring the strength of assocation

• Pearson’s correlation coefficient

Properties of r

• r > 0 indicates positive association.
• r < 0 indicates negative association.
• Extreme values r = 1 and r = -1 indicate perfect linear association.
• The value of r remains unchanged if the unit of measurement of X, Y, or both changes.
• r measures only the strength of linear association between two variables.

Class Activity

• Guessing Correlations
• Another Applet for Guessing Correlations

Fitting a line to data

• In general, no straight line will pass through all of the points.  We need a method for selecting the line with best fit.

Method of Least Squares

• Look at the deviations of the plotted points from the line in the vertical direction.  (Residual = observed - predicted)
• Compute the sum of the squares of the deviations.  (sum of squared residuals)
• Choose the line that minimizes the sum of squared residuals.  This line is called the least squares regression line

Computing the least squares regression line

• Body measurements (see neckwaist.csv and neckwaist.R in our Google Drive folder)

Please read Sections 8.1-8.3 for class on Wednesday.