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Show: on (10. 105) iii "the ifs{1’ Jambalaya (TI83+/8+5¢2Herplb+) Yea must know haw is ch» _ 1 L3) The: We went over Co ireisli’an (fa’08) w Fm» etc basic: :3 How Can We Summarize Strength of Association? _.
The Correlation ' , . i When the data points follow roughly a straight line trend, the variables are said to have an approximately linear relationship. In some cases the data points fall Close ’
to a straight line, but more often there is quite a bit of variability of the points around the straightline trend. A summary measure called the correlation de
scribes the strength of the linear association. HM
_ Correlation _
The correlation summarizes the direction of the association between two quan
titative variables and the strength of its straightline trend. Denoted by r. it'takes values between —l and +l. I A positive value for r indicates a positive association and a negative value for r in 3
dicates a negative association. I The closer r is to ii, the closer the data points fall to a straight line. and the
i stronger is the linear association.The closer r is to 0, the Weaker is the linear
association. E
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3 And we lookeci. at ﬂe‘éﬁAPlLS oh the next page — All this stuff {3
ahw‘l . ‘ LiNEAR association , If the D<~vcu~isiale (Explahaiw Variable) 3963 up) as“ the i
y~ Vanoblc (Response. Variable? also 03 56 up? @3o down 3’ i @ No real response? ._‘u
A} mean \u—t”
(/1 A FIGURE 3.7: Some Scatterplots and Their Correlations. The correlation gets closer .
to 5:] when the data points fall closer to a straight line. Question: Why are the cases in which
the data points are closer to a straight line considered to represent stronger association? the observations to units of euros or to units of thousands of dollars, We’ll get I
the same correlation. I Two variables have the same correlation no matter which is treated as the re
sponse variable. The correlation can be calculated by'statistics softwareand by many calculators. [a Then we used the TI caicuiai'or “to calculate the canola5091 J 7' i
for our GDP/Internet Use Scai‘i‘erPio'i‘ @ r= 0.888 592 1065 e 0.89) whit {dedicates a straw? partials Correlsizbn. V . _ 1;
[El Ami isolating at «Fig “ book eras/glee)” ohmic  Let’s get a feel for the correlation r by looking at its values for the scatterplots J .
shown in Figure 3.7: ' . The correlation r takes the extreme values of +1 and —‘1 only when the 2
data points follow a straight line pattern perfectly as seen in the top two graphs 5
in Figure 3.7. When r = +1 occurs the line slopes upward. The association is i
then positive, since higher values ofx tend to occur with higher values of y. The i
Value r = —1 occurs when the line slopes downward, corresponding to a nega :
tiVe association. ' 1' "Cm/l Riki) 5m 20 2.3 i In practice, don’t expect the data points to fall perfectly on a straight line. i  86113
However, the closer they come to that ideal, the closer the correlation is to 1 or ,
*1. For instance, the scatterplot in Figure 3.7 with correlation r = 0.8 shows a 6 l stronger association than the one with correlation r = 0.4, for which the data points fall farther from a straight line. ‘H Mongol. l4 Properties of the Correiation l The correlation r always falls between — 1 and + 1. The closer the value toi i
in absolute value (see the margin comments), the stronger the linear '
(straightline) association, as the data points fall nearer to a straight line. ' “i II A positive correlation indicates a positive association, and a negative correla— :'
tion indicates a negative association. . i f l The value of the correlation does not depend on the variables’ units. For ex‘ ' ' .9 ample, suppose one variable is the income of a subject, in dollars. If we change . If
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This note was uploaded on 12/30/2011 for the course STA 2023 taught by Professor Jones during the Spring '11 term at Tallahassee Community College.
 Spring '11
 Jones
 Statistics

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