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Grade 9

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.

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