Before we take up the discussion of linear regression and correlation, we need to examine a way to display the relation between two variables xx and yy. The most common and easiest way is a scatterplot. The following example illustrates a scatterplot.

Example 1

From an article in the Wall Street Journal: In Europe and Asia, m-commerce is becoming more 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. In the next few years, will there be a relationship between the year and the number of m-commerce users? Construct a scatterplot. Let xx = the year and let yy = the number of m-commerce users, in millions.

Table 1

x	y
2000	0.5
2002	20.0
2003	33.0
2004	47.0

Figure 1

A scatterplot shows the direction and strength of a relationship between the variables. A clear direction happens when there is either

You can determine the strength of the relationship by looking at the scatterplot 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.

Positive Linear Pattern (Strong)

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Negative Linear Pattern (Strong)

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Exponential Growth Pattern

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No Pattern

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Linear Pattern with One Deviation

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Negative Linear Pattern (Weak)

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In this chapter, we are interested in scatterplots 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 scatterplot. 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 xx is the independent variable and yy the dependent variable, then we can use a regression line to predict yy for a given value of xx.

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Last edited by Connexions on Jun 26, 2008 3:36 pm -0500.