Defining and Visualizing Correlation

Defining and Visualizing Correlation

A correlation is defined as a measure of the extent to which to variables are linearly related. However, before we learn more about correlations, 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.

EXAMPLE 1


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? To construct a scatter plot, let x = the year and let y = the number of m-commerce users, in millions.

This is your data table.

This is your scatterplot (from the data in the table above).


PRACTICE 1

Amelia plays basketball for her high school. She wants to improve to play at the college level. She thinks that the number of points she scores in a game will go up in response to the number of hours she practices her jump shot each week. She decides to test what she thinks, and records the following data:



Now, construct a scatter plot and state if what Amelia thinks appears to be true. (The answer is at the bottom of this page.)

A scatter plot shows the direction of a relationship between the variables. Generally, the direction of the relationship can be either positive or negative. The direction of the relationship is positive if as one variable increases, the other variable increases as well, or if one variable decreases, the other variable decreases as well. The direction of the relationship is negative if as one variable increases, the other variable decreases. If as one variable increases or decreases, there is no change in the other variable, we say that these variables have no relationship.

You can determine the strength of the linear correlation by looking at the scatter plot and seeing how close the points are to a line. The closer the points fall to a straight line, the stronger the relationship.

When you look at a scatterplot, you want to notice both the direction and the strength of the relationship. Use the arrows below to scroll through some examples.

Answers

Answer to Practice 1.

Yes, Amelia’s assumption appears to be correct. The number of points Amelia scores per game goes up when she practices her jump shot more. See below for scatterplot.

References:

  1. https://courses.lumenlearning.com/introstats1/chapter/scatter-plots/

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