Chapter 12.12, Problem 5E

What is extrapolation when using a linear model?

The ordered pairs below give the median sales prices y (in thousands of dollars) of new homes sold in a neighborhood from 2009 through 2016. (2009, 179.4) (2011, 191.0) (2013, 202.6) (2015, 214.9) (2010, 185.4) (2012, 196.7) (2014, 208.7) (2016, 221.4) A linear model that approximates the data is y=5.96t+125.5,9t16, where t represents the year, with t=9 corresponding to 2009. Plot the actual data and the model on the same graph. How closely does the model represent the data?

Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.