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A Statistical Analysis of Facebook

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On July 6, 2011, Mark Zuckerberg confirmed the rumors that there are now 750 million Facebook users in the world.

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The blogger Ben Foster has compiled a table of user data from 2004 through 2011.

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Add the information released on July 6, 2011 to the data published by Ben Foster. Think about how these data can be represented graphically. Which type of graph would you use? Justify your choice.

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Create a scatterplot of the number of Facebook users over time where time is measured in the number of months since December 2004. Describe the scatterplot.

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Determine the most appropriate function (linear or exponential) to model these data. Consider the scatterplot, the correlation coefficient and the residuals. Be prepared to justify your choice. Do you think the function you found will be a good model for the number of Facebook users in 5 years? Why or why not?

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Mark Zuckerberg believes that the number of users is no longer of importance and that the rate at which people share using Facebook is what is important. Click the video link to see what he has to say.

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In the video, Mark Zuckerberg discusses an example that can be used to model exponential growth, where paper is folded over itself 50 times. If what he says is true, we do not have enough paper to model that. However, we can model the first few stages to get a better understanding of exponential growth.

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Write the function that would model the length of stage x. What will the height of our paper be at stage 50?

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According to NASA, the distance from Earth to the moon is 238,855 miles. How does the height of our paper compare with this? Recall that the height of our paper at stage 50 is

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Mark Zuckerberg says that the height of this paper would be tall enough “to go from here to the moon 10 times”. Is this true? Our paper will go from here to the moon and back more than 10 times!

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It seems that Mark Zuckerberg is aware that the number of Facebook users cannot continue to grow beyond the size of the world population. This may be the reason he is more concerned with the rate at which people share on Facebook. Do you think sharing will continue to grow exponentially? Why or why not?

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Ultimately, it is the amount of money that Facebook earns which will keep the company in business. Wikipedia reported Facebook’s revenues for the last several years.

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Assuming these data are correct, find an appropriate regression function to model the revenue. Be sure to consider the scatterplot, the correlation coefficient and the residuals plot.

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Is it reasonable to conclude that revenue will continue to increase at the same rate as shown in these data? Why or why not?

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