1.3 The Power of Visualizing Data - Trends

Example 1 a) Create a scatter plot. Year Number of Homicides Source: Statistics Canada, CANSIM table

b) Add a line of best fit and describe the correlation. Approximate the equation of the line. Graph slopes upwards to the right. Positive correlation. Most points (but not all) are close to the line. Moderately strong correlation. y-intercept is approximately 540. line rose approximately 90 units in approximately 10 years. Slope = 9 y =9x (x = 0 corresponds to the year 1998)

c) Another (more accurate) line of best fit is know as a median-median line. Determine its equation. Year Number of Homicides Source: Statistics Canada, CANSIM table Step 1: Split data into 3 equal sized groups. (middle can be different by 1) Step 2: Find median of each group 1 st Group x: {1998, 1999, 2000, 2001} Median = ( )/2 = y: {538, 546, 553, 558} Median = ( )/2 = nd Group x: {2002, 2003, 2004} Median = 2003 y: {549, 582, 624} Median = rd Group x: {2005, 2006, 2007, 2008} Median = ( )/2 = y: {594, 606, 611, 663} Median = ( )/2 = 608.5

1995  x = -3 y = 8.43x (x = 0 corresponds to the year 1998) d) Use the equation to predict the number of homicides in 1995 and y = 8.43(-3) y = homicides in  x = 12 y = 8.43(12) y = homicides in e) What year will the homicide rate be approximately 700 y = 8.43x = 8.43x = 8.43x x = 19 In 2017 there will be 700 homicides.

Example 2 Create a scatter plot corresponding to each set of data. Describe the trends. Gold Owned # of Pirate Ships There is a strong positive correlation between the wealth of a pirate and the number of ships they own. For every additional 25 gold pieces they are able to own 1 additional ship. # of Pirate Ships Vacations days (Last 2 years) There is a weak negative correlation between the number of ships they own and how much vacation time they take. For every additional ship they own they take approximately 40 fewer days off in a 2 year period.