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CASE 2.1 DATA SPAM variables. EXAMPLE 2.3 Bots and Spam Messages We think that a netbot that has a large number of bots would be capable of generating a large number of spam messages relative to a netbot that has a smaller number of bots. Therefore, we think of the number of bots as an explanatory variable and the number of spam messages as a response variable. We begin our study of this relationship with a graphical display of the two Figure 2.1 is a scatterplot that displays the relationship between the response variable, spam messages per day, and the explanatory variable, number of bots. Notice that 6 of the 10 botnets are clustered in the lower-left part of the plot, with relatively low values for both bots and spam messages per day. On the other hand, the botnet Srizbi stands out with the highest values for both variables. Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The 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 the point in the plot fixed by the values of both variables for that individual. Always plot the explanatory variable, if there is one, on the horizontal axis (the x axis) of a scatterplot. As a reminder, we usually call the explanatory variable x and the response variable y. If there is no explanatory-response distinction, either variable can go on the horizontal axis. The time plots in Section 1.1 (page 19) are special scatterplots where the explanatory variable x is a measure of time. APPLY YOUR KNOWLEDGE A FILE SPAM 2.5 Make a scatterplot. (a) Make a scatterplot similar to Figure 2.1 for the spam botnet data. (b) Mark the location of the botnet Bobax on your plot. 2.1 Scatterplots 81 SPAM 2.6 Change the units. (a) Create a spreadsheet with the spam botnet data using the actual values. In other words, for Srizbi use 315,000 for the number of bots and 60,000,000,000 for the number of spam messages per day. (b) Make a scatterplot for the data coded in this way. (c) Describe how this scatterplot differs from Figure 2.1. Interpreting scatterplots To interpret a scatterplot, apply the strategies of data analysis learned in Chapter 1. Examining a Scatterplot In any graph of data, look for the overall pattern and for striking deviations from that pattern You can describe the overall pattern of a scatterplot by the form, direction, and strength of the relationship. An important kind of deviation is an outlier, an individual value that falls outside the overall pattern of the relationship. linear relationship The scatterplot in Figure 2.1 shows a clear form: the data lie in a roughly straight- line, or linear, pattern. To help us see this relationship, we can use software to put a straight line through the data (We will show how this is done in Section 23)