Linear Regression and Correlation: Scatter Plotshttp://cnx.org/contenthttp://cnx.org/content/m17082/latest/m17082Linear Regression and Correlation: Scatter Plots1.82008/06/23 13:29:46 GMT-52012/06/27 14:29:32.019 GMT-5BarbaraIllowskyBarbara Illowsky, Ph.D.illowskybarbara@deanza.eduMaxfield FoundationMaxfield Foundationcnx@cnx.orgSusanDeanSusan Deandeansusan@deanza.eduConnexionsConnexionscnx@cnx.orgsdean billowskysdean billowsky cnxorgMaxfieldFoundationelementarystatisticsMathematics and StatisticsThis module provides an overview of Linear Regression and Correlation: Scatter Plots as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.enBefore we take up the discussion of linear regression and correlation, we need to examine a
way to display the relation between two variables x and y. The most common and easiest
way is a scatter plot. The following example illustrates a scatter plot.From an article in the Wall Street Journal: In Europe and Asia,
m-commerce is popular. M-commerce users have special mobile
phones that work like electronic wallets as well as provide phone and Internet services.
Users can do everything from paying for parking to buying a TV set or soda from a
machine to banking to checking sports scores on the Internet. For the years 2000 through 2004, was
there a relationship between the year and the number of m-commerce users?
Construct a scatter plot. Let x = the year and let y = the number of m-commerce users,
in millions.

x (year)y (# of users)20000.5200220.0200333.0200447.0

Table showing the number of m-commerce users (in millions) by year.
Scatter plot showing the number of m-commerce users (in millions) by year.

A scatter plot shows the direction and strength of a relationship between the
variables. A clear direction happens when there is either:
High values of one variable occurring with high values of the other variable or
low values of one variable occurring with low values of the other variable.High values of one variable occurring with low values of the other variable.You can determine the strength of the relationship by looking at the scatter plot and
seeing how close the points are to a line, a power function, an exponential function,
or to some other type of function.When you look at a scatterplot, you want to notice the overall pattern and any
deviations from the pattern. The following scatterplot examples illustrate these
concepts.In this chapter, we are interested in scatter plots that show a linear pattern. Linear patterns
are quite common. The linear relationship is strong if the points are close to a straight line.
If we think that the points show a linear relationship, we would like to draw a line on the
scatter plot. This line can be calculated through a process called linear regression.
However, we only calculate a regression line if one of the variables helps to explain or
predict the other variable. If x is the independent variable and y the dependent variable,
then we can use a regression line to predict y for a given value of x.