Investigation 1: Big Data
Data transmitted across the internet increases every year. The following table of data relates the number of years since \(2015\), \( x_1\), to the monthly average amount of IP web traffic in Petabytes (1 PB=1000000 GB) during that year, \(y_1\).
Data transmitted across the internet increases every year. The following table of data relates the number of years since \(2015\), \( x_1\), to the monthly average amount of IP web traffic in Petabytes (1 PB=1000000 GB) during that year, \(y_1\).
The first few data points here are actual collected data points, but the rest are projections.
Practice Questions
1) Find the best fitting exponential equation for the data and use it to project the average number of Petabytes of web traffic per month in the year \(2025\).
Hint: type y1~a b^(x1) in a new line under the data table to find the best fitting exponential.
The constants \(a\) and \(b\) are called parameters of the exponential equation, you can try to fit other types of equations as well, linear, quadratic, etc. \(R^2\) is called the correlation coefficient and is a measure of how well the data fits the type of function you are trying to match it to. The closer this value is to \(1\), the better the fit we have.
2) Explain why an exponential model is the best choice to model the data here.
3) What is the average yearly percentage of increase in web traffic? Where is this information located in your model?
Solutions to Practice Questions
Source: http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/vni-hyperconnectivity-wp.html
Investigation 2: The Rising Cost of Education
Sometimes it is not clear right away what type of function should be used to model data. The following table relates the number of years since \(1976\), \( x_1\), to the average cost of tuition and room and board at a private \(4\) year university during that year, \(y_1\).
Practice Questions
1) Experiment by fitting different types of functions to the data. Suggestions: Linear (y1~mx1+b), Exponential (y1~ax1^b), Quadratic (y1~ax1^2+bx1+c). Which type of function fits the data best? How do you know?
2) Use your model to predict what it will cost to attend and stay at a private four year university during your first year of college.
Solutions to Practice Questions
Source: https://trends.collegeboard.org/college-pricing/figures-tables/tuition-and-fees-and-room-and-board-over-time-1976-77_2016-17-selected-years