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1 Introduction2 Graphing Distributions3 Summarizing Distributions4 Describing Bivariate Data5 Probability6 Research Design7 Normal Distribution8 Advanced Graphs9 Sampling Distributions10 Estimation11 Logic of Hypothesis Testing12 Tests of Means13 Power14 Regression15 Analysis of Variance16 Transformations17 Chi Square18 Distribution Free Tests19 Effect Size
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4.3 Guessing Correlations

This section is an interactive demonstration. The live simulation runs on the original site: open the demonstration at onlinestatbook.com.

Learning Objectives

  1. Learn how to estimate Pearson's correlation coefficient by viewing scatter plots.

Instructions
This demonstration allows you to learn about Pearson's correlation by viewing scatter plots with different values of Pearson's r. In each case, you will have an opportunity to guess the correlation. With a little practice, you should get pretty good at it.

Illustrated Instructions
The demonstration begins by displaying a scatterplot (shown below) and you guess what the correlation of the data in the scatterplot is by selecting one of 5 options below the graph.
Screenshot of the correlation-guessing simulation: a scatterplot of about 250 points, x and y both roughly 20 to 85, forming a broad round cloud with no visible tilt. Below it, the prompt The correlation is: with five radio buttons — -0.63, -0.29, 0.04, 0.37, 0.71 — and a New Data button.
As can be seen in screenshots below, once you select an answer you will be prompted whether the answer is correct or incorrect. Click the "New Data" to get a new dataset.
Screenshot of the same simulation answered two ways, side by side. On the left, labelled Incorrect Answer, -0.29 is selected and a frowning face reading Incorrect appears. On the right, labelled Correct Answer, 0.04 is selected and a smiling face reading Correct! appears — the round untilted cloud really does have a correlation near zero.

Guess the correlation of the data in the scatterplot by selecting from the options below the graph. You can change the data by clicking on the "New Data" button.

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.