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Statistics, Describing Relationships note

by: Schinedy Ductan

Statistics, Describing Relationships note

Marketplace > Mill Valley High School > Math > > Statistics Describing Relationships note
Schinedy Ductan
Mill Valley High School
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About this Document

This covers the basics of describing relationships.
Kenneth Spohn
Class Notes
Math, Statistics




Popular in Statistics

Popular in Math

This 2 page Class Notes was uploaded by Schinedy Ductan on Monday October 17, 2016. The Class Notes belongs to at Mill Valley High School taught by Kenneth Spohn in Fall 2016. Since its upload, it has received 4 views. For similar materials see Statistics in Math at Mill Valley High School.


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Date Created: 10/17/16
Describing Relationships 3.1 Scatterplots and Correlation The Principles ● Plot the data, then add numerical summaries.  ● Look for overall patterns and departures from those patterns.  ● When there’s a regular overall pattern, use a simplified model to describe it. Explanatory and Response Variables ● A response variable measures an outcome of a study. An explanatory variable  may help explain or predict changes in a response variable Displaying Relationships: Scatterplots ● The most useful graph for displaying the relationship between two quantitative  variables is a scatterplot. ● values of one variable appear on the horizontal axis, and the values of the other  variable appear on the vertical axis. ●  Each individual in the data appears as a point in the graph Form a Scatterplot 1. Decide which variable should go on each axis. 2.  Label and scale your axes.  3. Plot individual data value Describing Scatterplots  ● The graph shows a clear direction: the overall pattern moves from upper left to  lower right. ● The form of the relationship is slightly curved.  ● The strength of a relationship in a scatterplot is determined by how closely the  points follow a clear form. ● Outliers fall outside the overall pattern Positive and Negative associations ● Two variables have a positive association when above­average values of one  tend to accompany above­average values of the other and when below­average values  also tend to occur together. ● Two variables have a negative association when above­average values of one  tend to accompany below­average values of the other. Measuring Linear Association: Correlation ● A scatterplot displays the direction, form, and strength of the relationship  between two quantitative variables. ● Linear relationships are important because a straight line is a simple pattern that  is common. ●  A linear relationship is strong if the points lie close to a straight line and weak if  they are widely scattered about a line.  ● The correlation r measures the direction and strength of the linear relationship  between two quantitative variables. ● The correlation r is always a number between −1 and 1 ● Correlation indicates the direction of a linear relationship by its sign: r > 0 for a  positive association and r < 0 for a negative association.  How to calculate the correlation r: use the formula Facts about Correlation 1. Correlation makes no distinction between explanatory and response variables.  2. Because r uses the standardized values of the observa­ tions, r does not change  when we change the units of measurement of x, y, or both. 3. The correlation r itself has no unit of measurement. ● Correlation does not imply causation. ● Correlation requires that both variables be quantitative, ● Correlation requires that both variables be quantitative, ● A value of r close to 1 or −1 does not guarantee a linear relationship between two variables. ●  the correlation is not resistant: r is strongly affected by a few outlying  observations.  ● Correlation is not a complete summary of two­variable data,


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