5-7 Scatter Plots and Trend Lines

[Pages:6]5-7

Scatter Plots and Trend Lines

You can determine whether two sets of numerical data are related by graphing them as ordered pairs. If the

two sets of datVa oarce areblatuedla, yrouymay be able to use a line to estimate or predict values.

A scatter plot is a graph that relates two different sets of data by displaying them as ordered pairs. Most scatter plotRseavrieewin the first quadrant of the coordinate plane because the data are usually positive numbers.

A scatter plot is a graph that relates two sets of data. Plot each

y

You can uosrdeesrecdaptateirropnltohtesgtraophfinatdthtereringhdtstoinmdakaetaa.scTathteer pslcoat.tter plots below show4 the three types of relationships

that two s1e.ts(2o, 3f)data may have.

3 2

2. (21, 22) 3. (0, 2) 4. (22, 0)

1

5 4 3 2 1O1 2

x 12345

3

4

Vocabulary Builder

correlation (noun) kawr uh LAY shun

Related Words: correlate (verb), relationship (noun), relate (verb), scatter plot (noun)

PROBLEM 1D:tewfMioniqAtiuoKanIn:NtAitGiceosA.rrSelCaAtioTnTiEsRa mPLeaOsuTreAoNf DtheDsEtrSenCgRthIBoIfNaGrelIaTtiSonCsOhiRp RbeEtLwAeeTnION 1. The table shows the altitude of an airplane and the temperature outside the plane.

Example: The more a student studies, the higher the student's grades tend to be. So, there is a correlation between time spent studying and grades.

Use Your Vocabulary

Label each scatter plot positive correlation, negative correlation, or no correlation.

5. y

6. y

7. y

a) Make a scatter plot of the data.

b) What type of relationship does the scatter plot show?

0

x

y increases as x increases

0

x

y decreases as x increases

0

x

x and y are not related

Copyright ? by Pearson Education, Inc. or its affiliates. All Rights Reserved.

Chapter 5

HSM11A1MC_0507.indd 162

162

2/19/09 6:33:53 AM

2. Make a scatter plot of the data in the table below. What type of relationship does the scatter plot show?

When two sets of data have a positive or negative correlation, you can use a trend line to show the correlation more clearly. A trend line is a line on a scatter plot, drawn near points, that shows a correlation. You can use a trend line to estimate a value between two known data values or to predict a value outside the range of known data values. Interpolation is estimating a value between two known values. Extrapolation is predicting a value outside the range of known values. PROBLEM 2: WRITING AN EQUATION OF A TREND LINE 3. Make a scatter plot of the data pairs (year, attendance). Use a trend line to estimate the attendance at U.S. theme parks in 2019.

4. Make a scatter plot of the data below. Draw a trend line and write its equation. Use the equation to approximate the revenue in 2019.

5. Do you think you can use your model to extrapolate the revenue in 2050?

The trend line that shows the relationship between two sets of data most accurately is called the line of best fit. A graphing calculator or computer program can compute the equation of the line of best fit using a method called linear regression. The technology also gives you the correlation coefficient, r, a number from -1 to 1 that tells you how closely the equation models the data. The nearer r is to 1 or -1, the more closely the data cluster around the line of best fit. If r is near 1, the data lie close to a line of best fit with positive slope. If r is near -1, the data lie close to a line of best fit with negative slope. PROBLEM 3: FINDING THE LINE OF BEST FIT 6. Use an online linear regression calculator to find the equation of the line of best fit for the data in the table. Predict the cost of attending in the 2019-2020 academic year.

Causation is when a change in one quantity causes a change in a second quantity. A correlation between quantities does not always imply causation. PROBLEM 4: IDENTIFYING WHETHER RELATIONSHIPS ARE CAUSAL In the following situations, is there likely to be a correlation? If so, does the correlation reflect a causal relationship? 7. the number of loaves of bread baked and the amount of flour used

8. the number of mailboxes and the number of firefighters in a city

9. the cost of a family's vacation and the size of their house

10. the time spent exercising and the number of Calories burned

Quick Check correspond to 2003. What is the2coFrrinedlatthioenecqoueaftfiiocinenotf ttohethlirneee odfecbiemstafil pt.lLaceets9?5 correspond to 1995 and 103

correspond to 2y003. W0.5h2axt i?s th4e3.c9o9r;re0l.a9t9io0n coeffiycien0t .t5o2txhr?ee4d3e.9ci9m; a0l.9p9la0ces?

ES EXERCISES P35roblemN5S-a7omPlPrveariac_n_ctg_it_cic_e_e_a_Wn__doF_o_rPr_k_rms_oh_ob_er_elee_et_mx_e__rSc_io_s_el_vs_,i_sn_eg_e_E_x__tr_a__SF_ko_i_lr2l_0ma_0n_o0_dr_eW_e_o_x2_red0_r_c0P1i_1sr?_eo6_sb._,lT_esr2eme0en0PdE2rxalitncrtaeics2Se0k.0il3l2a0n0d0

Word Problem PrPaectricieo.d ________________

2001 2002 2003

Response Speed (s) Response SpeeGdes(tsa)tion (days) Gestation (days)

Response Speed (s) Response SpeeGde(sst)ation (days) Gestation (days)

Subscribers (millions)

Subscribers (millions)

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may ee

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Subscribers (millions)

GO for65 0

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H6y0el?p 52.5 Y2e(xar? 91)

3.

55

NBA Players

3.

50

Subscribers (millions)

65 0 10 20 30 40

0

y60? 45.5

5'264y900.05?00 '19L02Y2o0e(nxagr'9?e4v1i95ty.1'79()y61e(axr's9?)8 Memory Test

N82B00A0Players

5)

4.

and Gestation

0 10 20 30 40

y60?0

Longevity (years) 100 15.71(x ?

5)

400 Memory Test

Points per Game Points per Game

s, y

ese on

3. 3.

Points per Game

22 20 18 16

22 0 '90 '92 '94 '96 '98 y ? 52.5 Y2e(xar? 91) 20

NBA Players

18 3.

50

60 0 10 20 30 40

0 40'90 'L9o2nge'9v4ity ('y9e6ars')98

y 4.

y? ?2502.5

100Y2e(xar?159.711) (x

?

Memory Test

NBA Players

5)

4.

4.

80200

60 0 10 20 30 40

40 Longevity (years) y ? 100 15.71(x ? 5)

20 Memory Test

16

800 1 2 3 4 5

L3 L4

L2

5.

Points per Game

5. Gparrayk2211p2086s?0h. Ft1ihn6ed7.4d0aaGntaaem70qi2ne.u6sat4Pht7(ilexoa4ynt?eadfbo76le6r9ab.9et)r5loe. nwGdfrolayirnp221?0eth208hote1hf6aet7.th4dt0eeaGndt642aydaam0007a0t?i2anne.6.sct84ePhS57(leSaxea4tnyteu?eadddbl?yer76leef6T19tv5.ib.em9.en2)elu5o(e(wmxaift?not)rh1te)hmeeattenyd08642a0000?nc8e51Satnudd?yr2eT1v5iem.n2e3u5(e(mxait?n4t)h1e)m5e

L1

parks1.6Find an e0quatio1n fo2r a tr3end l4ine o5f the data. See left.

(billions of dollars)

L3

es

L3

L4

L2

5.

3L110 330 e (mL3illions)

6(x of Lines ? 280)

Revenue

51. 7890SGGpy1O....oR(daA(0000YU90rYbm?rRoteeaty..oCiek00tvllEiaplalel:ws?e0aAi7rlh.Ironinnwro2.Ftdnts5tutwe17ni)hesaenr0s6.nnenPod)7a.Hdc4fdt02eSaia0oAaGcA9nn.nhtt00aatocatemlt67oee0qAei2l1(3.n21ne.xcs(7un961soms89d.oadt9m440?09Phcati5ai7(5lilaenfxloan4oti32coyi1nrtco13?e28ea7nea9n90d9fb0.s9daoo997a06l)a)6fne66rnt9Aadadb.m1u913eR8tpu9R)9r0l.des94oee9e0a5v7mnvw7tS.eeeOde.R(dGpA(nYUnfn1bm1Rooea3lt8uet9uCiWriY9tvPr0lrlnE.iaeay9lle7eel:ak9ee0airletp8Ironabi8ansnh?rk0aoh.rdntosstCueetnF)saoa1fter1Us13inaUn9dhn9ton)90da.6et.hec9.S1f9dtt:S97.eAie9ea.4o9Ad.0ttannTtdgaGTtArynadh-2taath32l9ataec9ae0teA0?e10mtt71a.n2n04i0mqse7i670om29s1.n81c0de.n.uno0986e4se09escaSadt5.54i9PhanSPat2aeP327(5t9iletnc0axioan1e104auo.e20ydr67ntc990nrd1?k9ea1l.ek?91ayeo99rd0fsbs6efno9f7aT16l2tAve6d6r2n35.i990mem102ad.b..3R80n9u920941ee0.2tesuR9254)9erl0(ve7oeme(9mxe21nvw7e32an00nied201t?n30t.f8un2093t1o)lP03.ehu3i979a1rn0e8er9a)ketm8hstaoa1eetU3n9f910aUd..9tS919th.A99t.Sete9Tt.nrdh2Tay3dc09ae0h21ta.ti0?me067oan00mn.ecs08e.eSP25319Sae0aP21t.n0er0a6u9dk10rdlsk?1yer2se2fT13t9v025.i2.em009.4n220e3u25(e(21m3x020a2i00.t?n23430t)h31e)m5e

(billions of dollars)

Revenue

? Pearson Education, Inc. All rights reserved.

cinLOoSey6.y1temxidrei(n3ntx(nep1mlia0g?lniorlletEi32aoq38nnu00s5dma))tE.aio3oqtG5nnausr2.taaahUSGnpt-OodR(d78A(iUosbyhmoR..otetCT00eoCiltvllEi?ndhhlletl:weailtIaehoninnwrohAp7ipodntsurewen)2.tstaeaer5fGtes.n7nPedo)nrar0Hecanftaa6eSidqdopct2nha0Tahuaa9on.Lrsl.o00aciAelin6.2etncs7enso(8i3.ox(ma4o01mcdtri0B?anhfioEtloiLelroqi2t3d27aoniuo93ny.8tndo9a00a0afsLetat)Aib)eaopmnuln38puepgs0.ds4ter0aabhmGtoneoeeo.dSGxnOtlfoR(d3tA(8oUiToWbmP0Raotem.twho7Ciawe0tvllEierwlPblel:wekailaiIonaiswCnrnwroftdonatnsu.Gwe3onPne9d)saderH0dser..nrnPa1o)a:S9taAHcacfpthttehStitohghcorenh-aos39aeoc9l01.ltloc.4iAe67olob1.2csn7mnso8os.o.m40fgcod3i9afrt1oty.ahi6r9o2d7anl9ao.edo9t0aaffn3t9Auaa2.gpm9u4d38tpu1a0.hds4te0a1em1t3.oe0-e2.n.Wf233t8WeaP0.b7ae0rpbCkosCadoae3nn9d:0de.ad1:9tAagatt-tg9r.-a039c490F1t1.4i67oi1nns.d391.a69n

324 322

equation

9.9 10.3

for

a

trend

line

of

the

(%)

53LWinheaart

6

dy8 5

EquatiABoong3dse5ya2(nmLdeonTnghCtthehhi)ar(pGitnre.a)rp6hs81L.0inea1r 1E2.q7u5atio1n53s.5and1T64h.7eir

5 G2r0a.p1hs

6 22.2

8 26.5

9 29.0

? Pearson Education, Inc. All rights reserved.

ld9 1

6

4

9

5

anac

and draw a trend line.

16. Write the equation of the trend line

that you drew.

4 5 6 Dle7ongy8tohu9otfxhain3k-yyeoaur-cooludldpaunsdeay?our trend line to approximate the

ge (month)

to

Circumference (cm) 9.3 9.5 16 18.8 25 25.6 29.5 31.5 30.9 39.5

a. Graph the data. See margin. b. Find the equation of a trend line.

t6h1.7GtE9h0sretaicmpihtai6babette)h1se). 3eNPitlnG.hoFEredeecdPabcdtwrwias..h.co...natatieaWFGpFUoiCpYv.pdnpiofriiuoetmfirscnnCiahtohrprflaetraaddabeakiarieuptactntmyglttyatttlheiaitoeahhhhodosaleetubeeteenonreliTheeraoqetadethealsionedsUvhoqnuiinaidqnsetwuf1afedsamhaaukro5ae.ttalettiahfT0tFlaenaagtiite,etstfihoogive0nheoflomfenoo0nnerdrJon0WprupuTdooraUar,etemletfa0ffayoonAhcomrt0ntoa1abuigaeavtp0ethripf3eeletyttce.qramdeertmaruery7teutheward1?rlhiroa6dapnaeittgea5biln.afhSittteed4eebc4euvh.idiemtriotneqar,alJSnaeel6ainertuatunitnrrSehievr5funllgead(feyeeaweees0a?rohat..esFlrefli,irnsegtmao)e0tlw.ouhcaotgemn0fhntaneme0foaeeamarrdJPJdbegbblAruclrueeteiilievtheEnllreanaroyceyceaens.irupstc?atao4temtiigntefe2mftSaefn.irbmyt8etptenuheAi2reoea111YsweoeCnpErntl999ennaislfUep999fiteaic(ttuiit123tnrureirfenamehthiroasl..otce)faeetifapottud4h111evdift5r222MSedae7ae245tct5darPati,,,m8947oalaaaotye528Ftne.pg.na648.suoa.ed(lfbta3Jhott.u1112Fiohuoe2335lutenym901xs1,,,ao169aa?4tn909lfened765clslonerCE1maonyasmxxfootsc)npeuritEanptgtreraatunhceeimirndliosertsosgepnhceauers.trfdtso7sirmLeueoofoabdcruLanpmtyoeitikiltpnhtaanesu0ocnigdo?dutoegieafGeasptflsuetttoegi7ahidgtnooimeh5vencgnetoesea0ehrsoataqeaoFeilsrnnuqopudf.sdgaucrhuitanteahrtyotamtfhieroatoe.eecrnIcnettitoitssies in the table

1860

Baltimttohoerpsereeddaictta?thEexppolpaiunl.atSioen7e6in.m82a0r2g5inf.rom

Atlanta

78.6

41.841994 48.611995

14. a. Open-Ended Make a Jacksaonlivniellaer function. Use

taabg8rl1ea.3pohfidnagtcaaflocrulator52.761996

127,049 128,294 129,504

133,27890? at the poles.

134,510Exercise 11 The r-value rounds to 135,7241,000 since its value is

Washtiongfitnodn,thDe.Ce.quation of th7e8.l9ine of best fit. 39.001997 130,783 137,0010.999808967.

Today

Bobst.oWlinnheaatr idsatthae?coar?rebl.atSioenec7mo3ea.5frfigciine.nt for your43.811998

Miami 1SO5U.RCWE: TriimtienAglmWanahcat kind of

data for the following

82.5 trend line

do

you

think57.551999

comparison would be

2000

132,030 133,277 138,054

138,218 139,414 143,368

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ses, ar7e.

16. Graphing Calculator A school collected data on math and science grades of nineAravnedraogmelyTesemlepcetreadtustruedseinntNs.orthern Latitudes

Latitude (? N) 0 10 20 30 40 50 60 70 80

Student 1

2

3

4

5

6

7

8

9

Temp. (?F) 79.2 80.1 77.5 68.7 57.4 42.4 30.0 12.7 1.0

y ?1.06x ?Ma9t2h.31.; ?07.6970 89 84 79 94 71 79 91 84

Science 82 94 89 89 94 84 68 89 84

8.

Retail Department Store Sales (billions of dollars)

5.31 Year a. U1se98a0gra1p9h8i5ng c1a9l9c0ulat1o9r94to fi1n9d95the1e9q9u6atio1n99o7f th1e99li8ne of best fit for

vary. mall

Sales

b. tChreit8id6caatlaT. h1ai2n?6kbi.ngS1e6Se6hloeuflt2d.1t7he e2q3u1ation24f5or th2e6l1ine o2f7b9est fit be used to

h on

TECHNOLOGY GSOoUtRoCEw: Swtawti.sPtHicSaclhApobroselt.rcdaoicmct tofofgrtrhaaendUuenpsidt?eadtEeS.xtaWptleeasb.inCo.de: atg-9041 y 170.1.670U.xGsr?eapa7h7ign2rg.6aC6p;ahl0c.iu9nl9ag1tocraUlcsuelaagtroarphoinrgocnallciunlaetolrintoefianrdrtehge reequsastiioonnocfathlceulilnaetor

to

find

the

equation

of the line

of best

fit

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Year

1980 1984 1988 1992Gre1e99ti4ng 1C9a9r8d Sa20le0s2

ySOT(UsRiemC?Ec:eoI1nn.td6eS(rYs3nba)eaxilaltelio?rison4na25ls2S5)k6at.i7n4g61$3;U942n8?.2i9o0n.741$2094459.60

1991 420 $5.0

1992 395 $5.3

10.

SOURCE: Greeting Card Association

y 0.3A7vxe?rag2e8.M66a;le$1Lu2n.0g4Pboiwllieorn

1993 382 $5.6

1994 402 $5.9

near

Respiration E(qbureaatitohnss/manind)

The5i0r

Gra3p0hs

25

20

18

16

14

1995 $6.3

1996 $6.8

1997 $7.3

1998 $7.5

Heart Rate (beats/min)

200 150 140 130 120 110 100

SOURCE: Encyclopeadia Britannica y 2.64x ? 70.51; 0.990

11.

Wind Chill Temperature for 15 mi/h Wind

Air Temp. (?F)

35 30 25 20 15 10 5 0

Wind-Chill Temp. (?F) 16 9 2 5 11 18 25 31 y 1.35x ? 31.42; 1.000

Lesson 6-7 Scatter Plots and Equations of Lines 353

353

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