Two Regression Lines Suffice to Determine "r[superscript 2]" and "r"

The Pearson correlation coefficient can be recovered from the two least squares regression lines y[with circumflex] = b[subscript 0] + b[subscript 1]x and x[with circumflex] = a[subscript 0] + a[subscript 1]y without any data. This can be done both algebraically and geometrically. This can be done w...

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Bibliographic Details
Published in:	Educational research quarterly 2021-12, Vol.45 (2), p.21
Main Authors:	Sarkar, Jyotirmoy, Rashid, Mamunur
Format:	Article
Language:	eng
Subjects:	Algebra Correlation Equations (Mathematics) Geometry Information Utilization Introductory Courses Least Squares Statistics Problem Solving Regression (Statistics) Scaffolding (Teaching Technique) Statistics Education
Online Access:	Get full text
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Summary:	The Pearson correlation coefficient can be recovered from the two least squares regression lines y[with circumflex] = b[subscript 0] + b[subscript 1]x and x[with circumflex] = a[subscript 0] + a[subscript 1]y without any data. This can be done both algebraically and geometrically. This can be done without data even when the scales of the variables are different. The authors conclude with ways to use such information during instruction to help scaffold student understanding, number sense and problem-solving skills.
ISSN:	0196-5042