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An activity from a university mathematics course, math 116, focused on understanding relationships between variables through scatterplots and correlation. Students will learn the terminology and ideas for looking at association between two quantitative variables, find and interpret correlation coefficients for a set of bivariate data, and work as a team. Instructions, learning objectives, criteria, resources, and exercises.
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MATH 116 ACTIVITY 6: Understanding Relationships between data - scatterplots and correlation WHY: Much of the use of statistics involves relationships between variables. It is important to understand the terms and ideas involved in describing such relationships in the same way that it is important to understand the terms and ideas used in describing distributions of single variables. LEARNING OBJECTIVES:
Association between variables, correlation Two variables are associated if certain values of one tend to occur more often with some values of the second than with other values. If we wish to use changes or values in one variable to explain changes or values in the other, we refer to them as the response variable - measuring the outcome (think of y in our usual use of function and graphing notation) - and the explanatory variable - measuring the cause or explanation (think of x in our usual function notation). For two quantitative variables, the standard picture is a scatterplot - explanatory variable on the x-axis, response on the y-axis, plot the (x,y) - pairs. [If there isn't an explanatory variable - we aren't explaining one by the other - either variable can go on either axis]. Patterns are described by form (linear, type of curve - general shape of graph), direction ( positive - variables increase/decrease together; or negative - when one increases, the other decreases; sometimes there is no fixed direction) and strength (how closely packed around the basic pattern are the data points?). Correlation is a measurement of the amount of linear (y = ax + b) association between two quantitative variables.
The correlation coefficient r is given by
using the “Linreg” command on our calculators, or using computer software. The formula says:
Some scatter Plots, showing the corresponding values of the correlation coefficient r