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1.3 The Power of Visualizing Data - Trends

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Example 1 a) Create a scatter plot. Year Number of Homicides 1998558 1999538 2000546 2001553 2002582 2003549 2004624 2005663 2006606 2007594 2008611 Source: Statistics Canada, CANSIM table 252-0051

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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 + 540 (x = 0 corresponds to the year 1998)

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c) Another (more accurate) line of best fit is know as a median-median line. Determine its equation. Year Number of Homicides 1998558 1999538 2000546 2001553 2002582 2003549 2004624 2005663 2006606 2007594 2008611 Source: Statistics Canada, CANSIM table 252-0051 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 = (1999+2000)/2 = 1999.5 y: {538, 546, 553, 558} Median = (546+553)/2 = 549.5 2 nd Group x: {2002, 2003, 2004} Median = 2003 y: {549, 582, 624} Median = 582 3 rd Group x: {2005, 2006, 2007, 2008} Median = (2006+2007)/2 = 2006.5 y: {594, 606, 611, 663} Median = (606+611)/2 = 608.5

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1995 x = -3 y = 8.43x + 540 (x = 0 corresponds to the year 1998) d) Use the equation to predict the number of homicides in 1995 and 2010. y = 8.43(-3) + 540 y = 514.71 515 homicides in 1995. 2010 x = 12 y = 8.43(12) + 540 y = 641.16 641 homicides in 2010. e) What year will the homicide rate be approximately 700 y = 8.43x + 540 700 = 8.43x + 540 160 = 8.43x x = 19 In 2017 there will be 700 homicides.

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Example 2 Create a scatter plot corresponding to each set of data. Describe the trends. Gold Owned # of Pirate Ships 1506 502 1005 2509 2008 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) 6150 1350 4450 1050 9250 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.

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