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1.3 The Power of Visualizing Data - Trends. a) Create a scatter plot. Example 1. Source: Statistics Canada, CANSIM table 252-0051. b) Add a line of best fit and describe the correlation. Approximate the equation of the line. - PowerPoint PPT Presentation
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1.3 The Power of Visualizing Data - Trends
Example 1
a) Create a scatter plot.
YearNumber of Homicides
1998 558
1999 538
2000 546
2001 553
2002 582
2003 549
2004 624
2005 663
2006 606
2007 594
2008 611
Source: Statistics Canada, CANSIM table 252-0051
500
540
580
620
660
700
1998 2000 2002 2004 2006 2008
Number of Canadian Homicides 1998 - 2008
500
540
580
620
660
700
1998 2000 2002 2004 2006 2008
Year
Number of Canadian Homicides 1998 - 2008
500
540
580
620
660
700
1998 2000 2002 2004 2006 2008
Year
b) Add a line of best fit and describe the correlation. Approximate the equation of the line.
Number of Canadian Homicides 1998 - 2008
500
540
580
620
660
700
1998 2000 2002 2004 2006 2008
Year
Number of Canadian Homicides 1998 - 2008
500
540
580
620
660
700
1998 2000 2002 2004 2006 2008
Year
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)
c) Another (more accurate) line of best fit is know as a median-median line. Determine its equation.
YearNumber of Homicides
1998 558
1999 538
2000 546
2001 553
2002 582
2003 549
2004 624
2005 663
2006 606
2007 594
2008 611
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
1st Group
x: {1998, 1999, 2000, 2001} Median = (1999+2000)/2 = 1999.5
y: {538, 546, 553, 558} Median = (546+553)/2 = 549.5
2nd Group
x: {2002, 2003, 2004} Median = 2003
y: {549, 582, 624} Median = 582
3rd Group
x: {2005, 2006, 2007, 2008} Median = (2006+2007)/2 = 2006.5
y: {594, 606, 611, 663} Median = (606+611)/2 = 608.5
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.
Example 2Create a scatter plot corresponding to each set of data. Describe the trends.
Gold Owned
# of Pirate Ships
150 650 2100 5250 9200 8
0
2
4
6
8
10
0 50 100 150 200 250
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)
6 1501 3504 45010 509 250
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.
0
100
200
300
400
500
0 2 4 6 8 10
