Statistics: Transforming Bivariate Data

Objectives

• Students will recognize that bivariate data can be transformed to reduce the curvature in the graph of a relationship between two variables.
• Students will use scatterplots, residual plots, and correlation coefficients of different transformations of bivariate data to determine which transformation is more effective at eliminating the curvature.
• Students will make predictions about the response variable using a transformed data model.

Vocabulary

• bivariate data
• correlation coefficient
• exponential function
• least-squares regression line
• log transformation
• log-log transformation
• power function
• quadratic function
• residual plot
• scatterplot
• square root transformation

About the Lesson

This lesson involves square root, semi-log, and log-log transformations of curved bivariate data using given data sets.

As a result, students will:

• Observe scatterplots, residual plots, and correlation coefficients of bivariate data.
• Transform data using square root, semi-log, and log-log transformations.
• Determine which transformation is more effective at reducing the curvature in the graph of two variables.
• Use the least-squares regression line based on the transformed data to make predictions.