 # Investigation: Correlation

Lesson

#### Group discussion

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$$190 Display this data in a scatterplot using a spreadsheet tool. Then fit a trendline to the data and display the equation of the line. #### Group discussion • Is this trendline accurate? Give reasons for your answer and comment on any factors that might be affecting the data. The next table includes the prices from 2010 to 2014: Average airline ticket prices (2010 to 2014) Year 2010 2011 2012 2013 2014 Price \180$$180 $\$170$$170 \160$$160 $\$155$$155 \150$$150
Plot this data on a separate graph, and display the equation of the trendline.

#### Group discussion

• 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?

### Outcomes

#### 9.D1.3

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.