AP Statistics Monday, 26 October 2015 OBJECTIVE TSW investigate the role of correlation in...
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Transcript of AP Statistics Monday, 26 October 2015 OBJECTIVE TSW investigate the role of correlation in...
AP StatisticsMonday, 26 October 2015
• OBJECTIVE TSW investigate the role of correlation in statistics.
• EVERYONE needs a graphing calculator.
• DUE NOW– Gummi Bear Project (assessment grade) at the beginning
of the period.
• READ– Chapter 6: pp. 150-166
• TODAY’S ASSIGNMENT (due on Tuesday, 10/27/15)
– Chapter 6: pp. 167-170 (3-5 all, 13-16 all)
Chapter 6
Scatterplots, Association, and
Correlation
Suppose we found the age and weight of a sample of 10 adults.
Create a scatterplot of the data below.
Is there any relationship between the age and weight of these adults?
Age 24 30 41 28 50 46 49 35 20 39
Wt 256 124 320 185 158 129 103 196 110 130
NO
Now suppose we found the height and weight of a sample of 10 adults.
Create a scatterplot of the data below.
Is there any relationship between the height and weight of these adults?
Ht 74 65 77 72 68 60 62 73 61 64
Wt 256 124 320 185 158 129 103 196 110 130
Is it positive or negative? Weak or strong?YES
POSITIVE ????????
The closer the points in a scatterplot are to a straight
line - the stronger the relationship.
The farther away from a straight line – the weaker the relationship
Identify as having a positive association, a negative association, or no association.
1. Heights of mothers & heights of their adult daughters
+
2. Age of a car in years and its current value
3. Weight of a person and calories consumed
4. Height of a person and the person’s birth month
5. Number of hours spent in safety training and the number of accidents that occur
-+NO
-
Correlation Coefficient (r)-• A quantitative assessment of the strength
& direction of the linear relationship between bivariate, quantitative data
• Pearson’s sample correlation is used most• parameter - r (rho)• statistic - r
y
i
x
i
s
yy
s
xx
nr
1
1
Calculate r. Interpret r in context.
Speed Limit (mph) 55 50 45 40 30 20
Avg. # of accidents (weekly)
28 25 21 17 11 6
There is a strong, positive, linear relationship between speed limit and average number of accidents per week.
r = 0.9963586779
Moderate CorrelationStrong correlation
Properties of r(correlation coefficient)
• Legitimate values of r exist in the interval [-1,1].
0 .5 .8 1-1 -.8 -.5
No Correlation
Weak correlation
The value of r does not depend on the unit of measurement for either variable.
x (in mm) 12 15 21 32 26 19 24
y 4 7 10 14 9 8 12
Find r.
Change to cm & find r.
The correlations are the same.
0.9181459495
0.9181459495
x 12 15 21 32 26 1924
y 4 7 10 14 9 812
Find r.Switch x & y and find r.
The value of r does not depend on which of the two variables is labeled x and which is labeled y.
The correlations are the same.
The value of r is non-resistant.
x 12 15 21 32 26 1924
y 4 7 10 14 9 822
Find r.Outliers affect the correlation
coefficient
r is a measure of the extent to which x & y are linearly related.
A value of r close to zero does not rule out any strong relationship between x and y.
r = 0, but there is a definite relationship!
Correlation does not imply causation
Correlation does not imply causation
Correlation does not imply causation
Correlation Coefficient on the Calculator
>> CATALOG >> DiagnosticsOn >> Enter
When you ask for a linear regression equation, the correlation coefficient r is also displayed.
Assignment
• Chapter 6: pp. 167-170 (3-5 all, 13-16 all)–Due tomorrow, Tuesday, 27 October 2015.