Use the lab10data (csv) (pasted at very bottom) from your last lab session to an

Question

Use the lab10data (csv) (pasted at very bottom) from your last lab session to answer the following question.

Calculate the correlation of x1-x5. Then convert the correlations to covariances and fill in the following covariance table. Round all answers to two decimal places.

Covariance x1,x1 =

Covariance x1,x2 =

Covariance x1,x3 =

Covariance x1,x4 =

Covariance x1,x5 =

Covariance x2,x2 =  

Covariance x2,x3 =   

Covariance x2,x4 =   

Covariance x2,x5 =   

Covariance x3,x3 =   

Covariance x3,x4 =    

Covariance x3,x5 =    

Covariance x4,x4 =    

Covariance x4,x5 =    

Covariance x5,x5 =   

QUESTION 2

Use the following covariance table to calculate the standard deviations of x1-x5 and the correlations between variables x1-x5. Round all answers to two decimal places.

Standard Deviation x1 =

Standard Deviation x2 =  

Standard Deviation x3 =   

Standard Deviation x4 =  

Standard Deviation x5 =  

Correlation x1,x2 =

Correlation x1,x3 =

Correlation x1,x4 =

Correlation x1,x5 =

Correlation x2,x3 =   

Correlation x2,x4 =   

Correlation x2,x5 =   

Correlation x3,x4 =  

Correlation x3,x5 =  

Correlation x4,x5 =

data for tables

x1 x2 x3 x4 x5 3.761142968 18.40129016 11.55554523 9.14248122 10.96434877 1.974187005 17.38919136 10.97254664 9.011179166 9.737707075 3.105779121 17.73938911 11.6641794 8.705094562 9.580303124 4.86945075 18.30330671 13.18053029 11.76809837 9.303488364 2.007364627 15.98724284 9.410273369 9.045648623 7.678854603 3.671368091 17.73244181 11.40425835 10.49852404 9.383869523 3.066964514 16.07573172 11.76273853 8.969593916 10.0113529 5.386050973 18.70263942 12.71112797 10.07298021 9.07680142 2.482455463 16.86772789 11.52576547 8.539276792 10.72137693 0.31840202 15.63279035 9.524114706 8.295257938 11.05654532 3.511916625 15.85151659 9.334450734 8.714628021 9.865989337 3.461725687 16.80663637 11.34259412 8.101754166 10.41429655 2.417378297 15.82774135 10.28254392 8.708308654 8.933248576 3.467161556 18.38081927 11.04253927 9.16355545 10.83697943 3.328171161 17.65618494 10.88287555 10.21036929 9.057651519 3.629820846 17.22163975 11.17686747 10.29182386 10.46900265 1.375792712 15.34130319 9.468208804 7.220501938 8.768202118 2.52540235 16.85959291 10.02267965 9.078215112 9.661319371 2.025758957 15.93191398 9.731556736 9.596025101 10.89666326 2.526620223 15.78302061 11.12074092 8.737047144 11.34259397 3.247988655 15.60911754 9.435873308 8.792237577 10.38179851 2.32611615 17.18441504 10.94917879 8.957705396 9.060981842 3.947407125 16.98396647 9.579355322 8.369495509 9.690696566 2.839541407 16.35837104 10.69062286 8.250867671 10.75510367 4.348172985 18.34515306 11.81846109 9.289938882 11.12730004 2.57938781 17.05840953 10.48012762 8.52138483 10.17159536 3.897167928 16.49936817 12.05417695 9.109710292 11.23998788 1.481799206 17.51818995 9.679024708 9.345384232 9.66066094 2.042448719 17.74589618 10.83056276 7.802446783 10.78609743 3.127089009 16.56528895 10.17158632 8.952214087 10.11450648 3.338686823 18.29853133 12.52363947 7.959608533 10.72316446 3.337183956 17.88729295 12.3428732 9.378445656 10.49996333 4.366529354 18.01420286 11.12757123 8.508433099 9.964024362 1.919999791 17.40345885 11.23430179 9.976590511 11.29809928 3.939586018 17.89260747 11.09092239 11.30036742 9.41949204 2.346851361 16.93327324 11.2607041 9.103910654 9.334056246 3.345600546 17.519692 10.86906531 8.232746368 10.53655139 1.398119522 17.99423404 10.62692484 9.104698945 10.43727827 4.880005708 17.7054408 12.70821256 8.91325383 11.2829065 2.088081675 15.90369008 10.629227 8.569201128 9.368604168 2.053535861 17.51065536 12.36424474 8.913667906 11.05775177 3.921617851 17.16224684 9.993441749 9.477502661 11.53967506 4.13442165 17.18855663 11.38242058 7.543824362 10.86822344 1.673704604 17.12610894 10.46727386 9.599730287 9.677442325 2.706157734 15.76568252 10.1261472 9.103874042 9.646219579 3.028171021 17.69937941 11.07881394 9.808131125 9.963806051 4.912507467 17.20263179 12.27014808 9.124985991 11.20908009 2.844147619 17.1550659 11.78932991 8.965857139 9.630007453 4.435752208 16.38407568 11.46658772 7.809868317 9.819083984 4.743943587 17.86579191 11.79434402 8.484678782 10.95374498 1.511425925 16.89311173 9.737897096 8.442781237 9.125524174 3.11268747 17.11455521 10.34718641 8.204626994 10.83092272 3.4815532 17.82143233 11.24175778 10.49207624 9.73353514 4.61392761 15.70070498 11.32318849 7.837656663 9.942244759 3.174493042 16.35483515 10.93991909 8.201062012 10.81139661 1.821220927 15.4769906 9.924924789 8.110240968 9.340849375 2.147512812 15.78850896 9.655233545 7.592879953 9.865716455 1.685844797 16.57959747 9.321485287 8.988408242 9.255544112 2.764475317 16.55242024 9.626888309 8.770705027 11.82964295 2.958565417 16.21576215 11.06822514 7.941755461 9.413976447 1.473133193 16.04023573 10.50957967 9.547772813 10.00966844 2.230728309 19.24453721 10.68470996 9.617418811 10.52374715 3.586225936 15.9216049 11.0543453 9.586861059 10.43864622 4.104023471 16.5541761 11.38975087 11.06922221 10.80565646 2.030925968 15.49480888 9.909323004 8.413323186 8.702768152 3.154422454 16.82807683 10.37845972 7.951580691 9.011328889 1.020565824 16.30737473 10.16564123 8.171386056 8.193403786 2.624682272 17.57224203 11.63260619 8.97749087 11.013623 2.634920563 16.74059737 12.43914638 8.592563189 10.55480041 1.590909746 15.64361191 10.21945295 8.838561457 9.410657802 3.227803273 16.37759089 10.9507758 9.49528764 8.658084386 3.284313872 17.09230328 10.90160524 8.87413407 8.356193036 3.385015281 16.58518621 11.39005546 7.432918703 9.425466042 1.383997019 15.47307177 9.26010976 7.095358773 9.9876533 4.547630201 16.04402528 11.59463307 9.026136798 11.22384401 1.189013905 16.94584226 10.54110736 9.203541241 10.54387788 3.32557885 16.07574852 10.67577682 8.218431914 10.61808931 3.049121646 17.83528583 10.85073506 8.073393676 11.13867883 3.094021516 17.26531266 11.8622514 8.363553983 10.12345375 4.588223282 18.17064111 13.25426047 7.593467877 9.923728976 2.141013679 19.02326548 11.60276258 10.45495061 10.81450063 2.194932335 15.05174972 10.27062578 7.722957879 11.24882633 2.16647384 17.2164002 11.94156868 7.820694877 11.21816739 3.451388917 18.81014706 11.48028133 9.859116896 10.96900159 2.062772564 16.78654582 10.88978038 8.792101739 9.491962465 2.562143183 17.58919829 10.08481148 9.125312081 9.053849597 0.636440305 14.51465807 8.217749474 9.481168434 11.58934121 3.615453308 16.47479196 11.05271337 8.79417219 10.57713031 2.48524189 16.31528616 11.52813225 8.105205068 9.858976058 2.767917534 18.01021364 10.80122954 9.490611233 11.26214248 3.300916401 16.55116691 10.08144092 9.187001021 10.08983913 2.621691411 18.03366339 11.14877663 9.497626547 10.49022981 3.089965235 17.69887452 10.84111948 9.989267237 9.301904444 5.107845487 15.881417 10.32350376 7.912627751 9.167337575 3.299860119 16.21451355 11.77311277 9.354516413 9.847680105 4.192248622 14.60904819 9.749843939 7.497095642 9.145106702 2.617575809 15.47261232 9.693368491 9.880367684 9.478656514 4.501676482 19.40911591 12.20200555 10.66071999 11.20281948 2.896401714 14.66475872 8.750510933 9.302523241 8.810997985 4.998799551 17.96730039 12.08980967 11.68642173 10.85134735 2.027578196 17.48324777 10.85609589 9.424797886 11.1448432 3.718724447 17.93516943 11.88779586 9.782885025 10.056159 3.270545298 17.05452697 11.45432182 9.907340716 9.189066811 4.951099944 17.43532703 12.44716775 9.431749222 10.81754017 3.277790858 16.43217191 10.98563335 9.626484099 8.507878767 2.696716156 15.16318132 9.244175481 7.937861441 8.552394132 3.908411228 17.6430825 12.8338193 8.196995066 11.44231995 2.557093519 16.00893551 11.11122114 7.357184202 11.24100464 4.382909518 18.35786502 12.62346751 10.88420782 10.70813445 3.747666164 16.91416827 11.32828178 9.422431994 9.872928528 3.895268397 16.82279157 10.0899854 10.00518496 10.28201167 2.226549193 16.41893998 12.20626321 8.061351667 8.445706547 3.824595151 17.23346437 10.88569666 10.715564 11.81349446 2.170755037 16.98723758 9.873688338 8.87832406 10.37826206 2.82777386 16.92991258 10.28244737 10.86579088 9.378416942 2.999224253 18.61082466 12.69912518 8.60948601 9.968197952 3.022514637 17.61741423 11.39465836 8.154945308 8.82857757 2.344990566 15.0394549 9.673761026 5.627725314 10.30624505 4.13078096 17.88652523 11.32409728 9.104545944 9.84220479 2.67224583 17.39954765 10.52906567 10.66564647 8.819680573 2.455024888 17.25857999 10.17088462 9.132108099 10.83294816 2.818316277 16.49026174 9.527773384 8.50217398 9.065068548 3.332491411 17.35796477 11.40242606 9.849848413 9.936886323 3.008383982 18.16293227 10.76293752 11.74694378 9.292588446 4.170975702 15.51228106 11.38493134 8.612880517 10.13976746 2.956007059 16.10028233 10.01057955 9.589622753 9.697222328 2.728557475 17.03587987 11.36212753 9.38001717 9.127335811 2.385985135 15.5005324 10.09132752 7.576788173 10.59735276 2.232372887 16.18285507 10.67751238 8.891247085 9.342480252 3.780384158 17.44413478 11.17847518 8.624593372 8.96885535 4.282634741 17.54399732 11.72707181 10.21252484 9.385651957 3.458423959 16.32435075 11.36774578 9.470754202 10.25298867 2.694576985 15.93105182 9.969047024 10.2882806 9.191422841 1.739641303 14.44564596 10.24486783 7.334420456 9.025147647 2.970164393 16.75192048 11.77906052 8.822341651 9.701995254 3.684123596 17.03966156 10.36964765 10.2713752 12.49999295 2.240742058 16.64630154 11.66413803 8.976085194 7.747258079 3.108159802 16.56788677 10.544601 9.636038634 11.71969182 4.970560971 17.54038137 11.72963119 10.50938803 9.399026153 1.349451412 16.63128811 9.209646607 10.53787613 10.46291934 5.742697663 18.06523144 13.27629068 10.86321037 10.5063762 3.320919446 17.92195759 12.71617525 8.755041082 10.94517185 2.781587568 18.04966516 12.02300861 8.523499819 8.767329029 5.395530181 17.76020233 13.00672998 9.811651145 8.806458028 2.27797893 16.65841488 10.5350708 8.621916486 8.482039418 3.318472047 16.87966709 12.15777121 9.194044289 10.74703923 4.810390418 16.61841808 11.86681524 10.62087947 9.765198825 2.637396977 18.38809355 11.18560113 8.894978765 9.030029303 2.771861381 16.36157957 10.01379617 8.972077886 11.17028917 2.721871506 15.77177757 11.43462489 8.900252231 9.072103102 3.828205948 17.24036638 11.27478844 8.41673986 10.80723439 2.966106043 17.75777276 11.02997698 10.2413837 10.70690462 2.981376799 16.55437339 10.92517401 9.714932809 8.584504049 3.268890559 17.07041689 12.33137415 8.010122674 9.751806316 2.801853637 16.55834823 10.11458927 8.804602922 9.811005947 2.901366907 16.48778331 10.00917146 8.659397485 9.857669071 2.819155274 15.92136959 10.4403626 7.812616645 10.04846063 2.458268017 17.50200865 10.96844757 9.92461332 11.22074283 3.529712372 17.02872857 10.65196803 10.31029425 11.61212093 1.657001526 17.95945962 10.66847349 9.192997031 9.895939175 1.562472917 15.6316523 10.31070479 7.170174786 7.242626722 2.523994654 17.61044315 10.98314888 8.97428381 10.44741215 1.498650765 17.82344668 12.41149233 8.156863872 9.918723422 4.33500964 16.59022951 11.07096908 10.35286155 9.010065328 2.497996774 17.12448084 10.21296868 10.01372072 10.07673179 1.857233901 16.19423395 11.36936652 8.032900925 10.36022794 2.030407101 16.72465605 11.24383708 8.755382372 11.97768381 3.290624531 16.02722452 9.897562491 8.720370851 10.22131507 3.411681855 16.48659746 10.55517238 8.708295815 10.96947527 3.219271845 17.22517057 12.99783305 8.584845952 9.90316864 3.28618907 14.81010855 10.4544695 7.321114947 8.370725314 3.074970825 15.57671905 10.35563106 7.690751547 9.889841522 2.853115943 15.87916402 10.18523286 8.086903143 6.955935807 4.999712446 19.37416187 13.50563258 9.554758351 10.4527282 1.621565963 17.43162248 12.10982073 6.802256207 10.18548243 2.422746115 17.98226195 11.36854209 9.169087278 10.27452528 3.921749415 18.49582776 12.88723996 10.61768135 8.829617518 1.773344647 16.26991101 10.49157128 9.11253322 9.512445706 2.798284526 17.95255675 11.07024569 8.212704427 9.770400489 2.17914645 16.99325847 11.28317853 8.48454988 9.602833296 1.496580557 18.29979695 12.38241585 11.39261832 10.01697554 3.646032938 16.43950928 11.1074585 7.544200271 10.07164639 1.855243325 18.04966757 10.5976874 9.82480867 10.97622891 1.6991641 17.4922128 11.09137554 8.907648967 10.2367907 1.548327623 15.69054213 8.888946521 8.290170146 9.974184924 2.761063805 15.88415054 11.0268453 8.345893835 9.446851062 4.875831024 16.87358229 11.4383107 8.252493228 10.78468676 3.242247633 17.69153504 11.26370934 9.783586575 10.42141753 3.194563669 16.0294583 10.35146707 10.06457424 10.6703058 1.981956828 18.00116995 10.71582393 10.17241733 8.488379693 4.357391931 17.78926075 9.560142763 9.590874963 10.86651284 2.154478102 16.69392634 9.481761897 7.585536902 7.559113338 1.722097812 18.23449835 10.44988886 9.836572831 11.31140879 3.650336352 16.21191428 9.07282331 9.785106353 10.03024022 3.306473905 18.59418168 11.46115152 8.464962744 11.37921717 2.422772787 16.74142547 10.81224287 9.056866595 8.095179717 4.354106259 18.33630535 12.55923507 9.687889444 10.91582251 3.896574231 16.76267001 11.67814096 7.424545529 8.616761275 3.355649244 18.49335912 12.85057047 9.246130038 10.70940368 3.852155041 17.1802726 10.69086159 9.519750743 9.172952609 2.289476525 18.16672756 12.45066033 9.732063421 11.48591186 1.854885966 15.78235693 10.72182291 6.686048472 10.64252802 3.407085735 16.73530698 11.96985366 9.62509402 8.869005526 3.256892495 16.49288313 10.10414106 8.668390549 11.28774315 2.954885328 17.85224362 11.37056022 9.450164523 8.509396203 3.090266035 17.10314449 11.50633958 8.806976189 10.24331098 3.894363783 17.77266726 11.49132429 8.602240588 10.74739696 4.674478651 16.76826558 12.12183849 8.152174762 11.53558159 3.380389566 16.9035719 11.0741482 8.228197048 10.14181097 1.823121755 16.31997471 9.04944528 8.002954185 8.087545692 2.375327866 15.81304724 9.964464925 6.938464954 10.67967507 2.868958558 17.48689993 10.8031558 8.02013599 8.870431541 2.595082323 18.48955641 13.00617133 8.452324435 10.07456981 4.073349736 17.06291274 11.61374269 8.377522941 8.577096015 2.327177046 16.57209184 10.22929405 9.050387141 8.42748945 3.674377854 15.66645132 11.02793796 9.358042507 10.03069608 2.488726155 16.29604203 9.91524655 8.585790296 9.389344053 1.11165093 16.02723149 10.32520013 8.030797992 8.0590967 2.425612051 17.02712703 10.82007525 9.332253622 11.64532613 4.248487292 17.79198923 11.88999378 8.749949786 11.98772768 1.703722848 16.20915053 9.64846115 7.847954175 10.3032391 2.547262257 16.05792674 9.260715773 7.963830433 8.315909957 2.808160502 17.37914588 11.15365547 9.56615188 10.0268958 3.932635086 16.81424457 11.28174151 9.390948049 11.68241612 4.252747675 18.10567521 12.28050753 11.91804607 10.79842451 3.6159236 17.3485517 11.22429524 8.652463398 8.472232306 3.394438895 17.01498332 11.0873723 9.907628005 9.231455384 4.136517912 18.30728444 12.88601237 9.405149227 11.2051944 3.190443783 16.51237428 10.99937107 8.394443813 11.24967427 2.221846966 17.0911158 10.59051603 8.739295341 10.66650166 4.01885442 17.92099455 9.719994817 9.741135175 10.83570123 1.268404957 17.71564726 10.39856511 8.889438544 8.96039739 2.599585447 17.24793943 10.62001677 8.322397678 10.18391315 2.470919674 17.58509784 11.04986956 10.24417004 10.10799541 3.923414607 19.43474952 12.57992655 8.638414193 9.745534748 2.252720638 19.521806 12.33641251 10.08592107 11.35832804 2.06223392 18.96319531 12.28666615 11.01190916 7.880026624 5.377692883 18.60056729 11.94976141 9.327704243 9.272759716 2.734652263 17.10748189 10.67753175 9.40163016 9.378753418 2.039551526 15.93657569 9.436452912 7.424702042 8.775949814 2.697521661 17.34834621 11.3521876 8.312769321 10.97078764 3.866255672 19.10104214 13.14216229 8.961439848 10.33605493 0.855467228 15.47699976 9.476018459 9.35255171 10.40299823

Explanation / Answer

Question 1:

Covariance x1,x1 = 1
Covariance x1,x2 = 0.3
Covariance x1,x3 = 0.5
Covariance x1,x4 = 0.25
Covariance x1,x5 = 0.16
Covariance x2,x2 = 1
Covariance x2,x3 = 0.63  
Covariance x2,x4 = 0.45  
Covariance x2,x5 = 0.21  
Covariance x3,x3 = 1  
Covariance x3,x4 = 0.22
Covariance x3,x5 = 0.18
Covariance x4,x4 = 1
Covariance x4,x5 = 0.11
Covariance x5,x5 = 1

Question 2:

Standard Deviation x1 = 1
Standard Deviation x2 = 1
Standard Deviation x3 = 1
Standard Deviation x4 = 1
Standard Deviation x5 = 1
Correlation x1,x2 = 0.3
Correlation x1,x3 = 0.5
Correlation x1,x4 = 0.25
Correlation x1,x5 = 0.16
Correlation x2,x3 = 0.63  
Correlation x2,x4 = 0.45  
Correlation x2,x5 = 0.21  
Correlation x3,x4 = 0.22
Correlation x3,x5 = 0.18
Correlation x4,x5 = 0.110

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