8. Two Variable Data Analysis

Lesson

For each of the following pairs of variables, discuss the strength and direction of the correlation (if any):

- The floor space of an office
**and**the number of desks that can fit - The number of students on an field trip
**and**the number of teachers supervising - The number of text messages sent
**and**the amount of prepaid credit remaining - The distance driven by a car
**and**the amount of fuel in the tank - The height of a person
**and**the number of hats they own - A household electricity bill
**and**the total income of the residents - The amount of internet data
**and**the age of the internet user

The average prices of an airline ticket on a particular route from the years 2001 to 2009 are shown in the table below:

Average airline ticket prices (2001 to 2009) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 |

Price | $\$280$$280 | $\$180$$180 | $\$270$$270 | $\$260$$260 | $\$240$$240 | $\$190$$190 | $\$230$$230 | $\$220$$220 | $\$190$$190 |

Display this data in a scatterplot using a spreadsheet tool. Then fit a trendline to the data and display the equation of the line.

- Is this trendline accurate? Give reasons for your answer and comment on any factors that might be affecting the data.

The next table includes the prices from 2010 to 2014:

Average airline ticket prices (2010 to 2014) | |||||
---|---|---|---|---|---|

Year | 2010 | 2011 | 2012 | 2013 | 2014 |

Price | $\$180$$180 | $\$170$$170 | $\$160$$160 | $\$155$$155 | $\$150$$150 |

Plot this data on a separate graph, and display the equation of the trendline.

- How does this trendline compare to the one above?
- Use the equation of each line to predict the average price of an airline ticket in the year 2015. What do you see?

Create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate.