16_20110214mon_stats_86728_p11

16_20110214mon_stats_86728_p11 - ,. __ \t I...

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Unformatted text preview: ,. __ \t I fifl.§5.i.._,_.__, From §2-5: 33. THE aware} -—,86?23 E. NQZ'é Eh “I?!” fwd “ I, and “ ” (EMPJHcaI ROI/‘6') and E "5" ("5"‘)) Mamba! :.N the *‘ z—scove.” is 619 Mm IMFTT coNCEPT. , , ' 13+ was as a. rulerfr Measmrx‘ bow far awag {Pm fire mean a Paarfltuiaf‘ "P 511% Porkfhgfs {I [El 0W Z~5cale {5 may} mmmfi[email protected] Jafd are, more ~or» [e55 Normal « a (2?, \, [(2] Example: Saga” Mort/Ma! 961%: My at 225.2 and @ S 2" Ba 7 New supydse a dab Po}th 3c} is 21.3) $9. ____ __ X: 21.5. QueerIbM Wharf is :85 E’zfiwfé? Answer; [13 The 3(0er (You. flusW _ x —v 35 on your w‘mla'br H- “ 5 N1 il look. like {3455* 3‘? HMS-J5 wromg w} {We [.3 —- 25.2. g:- “fim— 2: -1.054 054 @5492 *1:05 Buff wkff Aces. this MEAN The folloufna was dcswsscd m class and wriH-en—UP aflcr class. [a The E~SCOV8 gamma INDpCES a '2‘." soak: UF" the data. Ila effect. H‘ 5'\135 Q5 8 This a 55-5me 6“? Z= -~I.05 Would be 31mg"? ! Vlch I’ll"; «1 m3; 1 ""13 42 —1 7 Z M WE ‘ l . - 2 WithhhaLLfi-ormfirbn Declare; l1 Chg; “lijfifiiqe flier €[355- ______® I fin/two” ! F m {3.2: How Can We Exelore'llfl 14554615416} (if there is We) ‘ ézime Quaniaifve \faflbélei --—- (See 39. “(03 D; ' Morton! .u 11] Yet» We Si) H705 E D TO HAVE enl'ereol the 39 data paints [etclfi from the “Dismal” Column and fire “6D?” «CB/Lima fivm 73.1% 3‘4) De». 103), - Ve’i 5W W #- IF Y6U DIDN’TDO Tins FDR TADAYJ 3» rr Fae I is: W519! ! l i [,3] I 14564 these age «in cmsirwd at 56477512 15107" wsfmifer {2: he 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 i-reis-li’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 straight-line 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 straight-line 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 i l i 11 i 3 And we lookeci. at fle‘éfiAPl-LS oh the next page -—- All this stuff {3 ahw‘l . ‘ LiNE-AR 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 canola-5091 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 ' (straight-line) 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 ;: [a Waits} We R4 The Caicabi'er PM #8 Lrficar Hartman Like of ‘\ Basie Fit " {Br our dais. ...
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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.

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