Course 2, Unit 3 - Patterns of Association

Summary
In the "Patterns of Association" unit, students learn to describe the association between two variables by interpreting a scatterplot, to interpret a correlation coefficient, and to understand the limitations of correlation coefficients. They learn to know when it is appropriate to make predictions from the regression line, and to understand the effects of outliers and influential points on the correlation coefficient and on the regression line.

Key Ideas from Course 2, Unit 3

  • Least squares regression line: A line that fits a set of data, with slope and intercept chosen to minimize the errors (distance) between the actual data points and the line. This line also contains the point .
  • Squared errors: A point on the regression line represents a prediction about the y value (dependent variable) given the x value (independent variable). Since the points on the regression line are the result of using the regression equation, there could be a difference between the actual y value that occurred for this particular x value (the data point) and the predicted y value (the point on the line). These differences can be thought of as errors in prediction. They are visualized as the vertical gaps between given data points and the regression line. The sum of squared differences gives a measure of how well a line fits the data.
  • PearsonŐs correlation coefficient, r: A single number that gives a measure of the strength of the linear association between variables. Perfectly linear data will have an r value of 1 (for a positive association), or an r value of -1 (for a negative association). A set of data that is quite linear, and for which the y values increase as the x values increase, is said to have a strong positive association. If the points appear to fit a linear trend but the y values decrease as x increases, the association is negative. A set of data that is quite random, not at all linear, will have an r value close to zero.
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