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ORC Resource Number #1466
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The Regression Line and Correlation: The Centroid and the Regression Line
PROFESSIONAL COMMENTARY

In the fourth of four related activities (all accessible from this site), students work with bivariate data to investigate relationships between variables. The applet allows students to enter bivariate data on a coordinate grid using various scales. The applet then graphs the regression line, shows its equation, and indicates the correlation between the variables. Students then locate the centroid of the data by finding the mean of the x-values and the mean of the y-values. (author/sw)

CAREER APPLICATION

All career-technical students routinely gather data to analyze situations, make predictions, and report results of tests or experiments. Whenever two related items of mathematical data (bivariate data) are produced, the career-technical teacher and mathematics teachers can use this lesson to plot the data points on a graph, show the regression line, and find the centroid. Data such as weight and height, density and weight, diameter and length, age and weight, and stocking density and area are just a few examples of what can be plotted to scale by the applet in this resource. The input can be set as the independent variable and the output can be set as the dependent level. The scale of the x and y axes can be changed to show how the location of the centroid and regression line change as the axis is lengthened or shortened. Manufacturing Technologies instructors can use this resource to show where the centroid on a metal plate should be drilled. Mathematics teachers are encouraged to use the expertise of their career-technical students to gather and analyze data for illustration purposes in their mathematics courses.

OHIO STANDARDS
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Mathematics Academic Content Standards
Data Analysis and Probability Standard
NATIONAL STANDARDS
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Principles and Standards for School Mathematics
Data Analysis and Probability Standard
RESOURCE TYPE
Content Resource
STANDARDS ALIGNMENT
Grades 8–12
CAREER FIELDS
Agricultural & Environmental Systems;
Arts & Communication;
Business & Administrative Services;
Construction Technologies;
Education & Training;
Engineering & Science Technologies;
Finance;
Government & Public Administration;
Health Science;
Hospitality & Tourism;
Human Services;
Information Technology;
Law & Public Safety;
Manufacturing Technologies;
Marketing;
Transportation Systems;
General Career Skills
TOPICS
Mathematics --
Statistics;
Data analysis;
Technology;
FOUND IN
KEYWORDS
applet;
bivariate data;
line of best fit;
regression line;
correlation;
centroid
Publisher: National Council of Teachers of Mathematics