1.  Once data is collected and organized, we need to analyze the strength of the relationship and formalize it with an equation  By understanding the strength of the relationship, we can make estimates and predictions about the two variables being studied

2.  Graph with a few data points…

3.  Graph with a few more data points…

4.  Sometimes one data set will look more linear than another one  There are varying degrees of linearity  The more linear a set of data is, the closer the lines are to the line of best fit  We use the CORRELATION COEFFICIENT to represent how far the points are on average from the line of best fit  If r is close to +1 or -1, it’s a close fit  The sign of r relates to the slope of the line, not the fit

5.  The following diagram illustrates how the correlation coefficient corresponds to the strength of a linear correlation: 1 0.67 0.33 0 -0.33 -0.67 Perfect Strong Moderate Weak None Weak Moderate Strong Perfect

8.  Sarah researches the cost of houses in a new area. She is looking for:  A 2-storey, detached house  Asking prices of $300,000 or less  2000 square feet of living space

9.  The following square footage with house prices were found in the neighbourhood of where Sarah was looking to buy a house: XY 1700271,900 1850289,900 1600277,900 1650289,900 1700279,000 1800294,900 1550269,900

10.  Draw the line that you think comes closest to matching the trend.  Use the line to estimate how much a 2000 square foot house might cost in Sarah’s area.

11.  Sarah notices a new For Sale sign on a house in the area. At 2300 square feet and $384,500, it does not match her criteria. However, she decides to add the data to her collection anyway.  Draw the new line of best fit  Use this line to estimate the price for a 2000 square foot house in Sarah’s neighbourhood. Compare this estimate to your first estimate.

12. XY 1700271,900 1850289,900 1600277,900 1650289,900 1700279,000 1800294,900 1550269,900 2300384,500

13.  How did the arrangement of plotted data affect the way you drew a line of best fit? How does it affect your confidence in using the line to make predictions?  A real estate agent tells Sarah that 2000 square foot houses often come up for sale in this area, usually at prices from $295,000 to $305,000.  How close were your estimates to these prices?  Which line of best fit helped you make a closer prediction?

14.  What equation can we use to model the line of best fit?  y = mx + b  What does the y-intercept represent in this line of best fit? Does its meaning make sense in this context? Why or why not?

15.  Once you determine that two variables have a moderate to strong linear relationship, you can find a linear model.  This way, you can make predictions for one variable based on the value of the other variable

17.  p. 175 #1, 2, 7, 9, 13