<?xml version="1.0" encoding="UTF-8"?>
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<Startup-Code startupcode=""/>
<Task-table>
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<Task/><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Font size="22" encoding="UTF-8">Line\303\246r regression </Font></Text-field>
</Input>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Marius og Sophie har m\303\245lt sammenh\303\246ngen mellem et penduls l\303\246ngde og dets svingningstid. I nedenst\303\245ende tabel ses m\303\245lingerne:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Som vi diskuterede i 1.g, er et residual forskellen mellem en m\303\245lt </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==</Equation><Font encoding="UTF-8">-v\303\246rdi og en matematiske models </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==</Equation><Font encoding="UTF-8">-v\303\246rdi.
Hvis vores datas\303\246t best\303\245r af en r\303\246kke datapunkter </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation> og vores regression giver modellen <Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation>, er residualet for det i'te datapunkt givet ved</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Residualplottet viser grafisk residualerne for de enkelte datapunkter. Nedenfor ses datapunkter med regressionslinje indtegnet og det tilh\303\270rende residualplot.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Residualspredningen <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==</Equation> defineres som</Text-field>
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<Input><Text-field style="Text" layout="Normal">hvor <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGPg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGPg==</Equation>, <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LlEiLEYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRicvJSllcXVhbGl0eUdGTC1GRzYuUSJ+RidGPkZKL0ZORkxGT0ZRRlNGVUZXRlkvRmduRmVuRmluLUZHNi5RIy4uRidGPkZKRl5vRk9GUUZTRlVGVy9GWlEsMC4yMjIyMjIyZW1GJ0Zfb0Zpbi1GRzYuUSIuRidGPkZKRl5vRk9GUUZTRlVGV0ZZRl9vRmluRltvRkYtRiw2JkYuLUYjNiUtRi82JVEibkYnRjJGNUYyRjVGQEZDLyUrZXhlY3V0YWJsZUdGTEY+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LlEiLEYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRicvJSllcXVhbGl0eUdGTC1GRzYuUSJ+RidGPkZKL0ZORkxGT0ZRRlNGVUZXRlkvRmduRmVuRmluLUZHNi5RIy4uRidGPkZKRl5vRk9GUUZTRlVGVy9GWlEsMC4yMjIyMjIyZW1GJ0Zfb0Zpbi1GRzYuUSIuRidGPkZKRl5vRk9GUUZTRlVGV0ZZRl9vRmluRltvRkYtRiw2JkYuLUYjNiUtRi82JVEibkYnRjJGNUYyRjVGQEZDLyUrZXhlY3V0YWJsZUdGTEY+</Equation>  er de enkelte residualer, og <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==</Equation> er antallet af observationer.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Hvis en line\303\246r model skal v\303\246re god, skal residualspredningen gerne v\303\246re <Font bold="true">forholdsvis lille i forhold til variationen i de y-v\303\246rdier</Font>, som indg\303\245r i datas\303\246ttet.
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<Font encoding="UTF-8">Hvis der er et enkelt residual, der har en numerisk v\303\246rdi, som er betydelig st\303\270rre end residualspredningen, karakteriseres det tilh\303\270rende datapunkt ofte som en </Font><Font bold="true">outlier</Font><Font encoding="UTF-8">. Det er altid en overvejelse v\303\246rd, om en outlier kan skyldes m\303\245lefejl. Det kan eksempelvis v\303\246re, at man ikke har holdt termometeret nede i den v\303\246ske, man m\303\245ler temperaturen p\303\245 ved netop dette m\303\245lepunkt.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Jomaa og Patricia har m\303\245lt sammenh\303\246ngen mellem den hastighed, som en kugle falder med, og den tid den er faldet. I nedenst\303\245ende tabel ses m\303\245lingerne:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Det antages at hastigheden kan beskrives som en line\303\246r funtkion af tiden.  </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">a) Lav line\303\246r regression, et residualplot og beregn de enkelte residualer</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi indl\303\246ser datas\303\246ttet: </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Residualspredningen er beregnet sammen med residualplottet. Hvis man kun skal bruge residualspredningen kan den beregnes ved: </Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Residualspredningen for den line\303\246re regressionsmodel er 0,44. I datas\303\246ttet ligger y-v\303\246rdierne i intervallet [1,0;9,3]. Dvs. spredningen p\303\245 residualerne er kun en br\303\270kdel af y-v\303\246rdierne og bliver aldrig st\303\270rre end nogle af y-v\303\246rdierne. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Dette understreger ydereligere, at den line\303\246re model med forskriften  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JlEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiYtRiw2JlEidEYnRi9GMkY1RjIvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RicvRjZRJ25vcm1hbEYnRjJGQy1JI21vR0YkNi9RIj1GJ0YyRkMvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZLyUpZXF1YWxpdHlHRjQtSSNtbkdGJDYlUSU5Ljk1RidGMkZDLUZGNkFRMSZJbnZpc2libGVUaW1lcztGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEzRicvJSVib2xkR0Y0L0YwRjQvJSp1bmRlcmxpbmVHRjQvJS5zdHJpa2V0aHJvdWdoR0Y0LyUqc3Vic2NyaXB0R0Y0LyUsc3VwZXJzY3JpcHRHRjQvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lJ29wYXF1ZUdGNEYyLyUpcmVhZG9ubHlHRjQvJSljb21wb3NlZEdGNC8lKmNvbnZlcnRlZEdGNC8lK2ltc2VsZWN0ZWRHRjQvJSxwbGFjZWhvbGRlckdGNC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGNEZARkNGSUZLRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5GZXFGZm5GPS1GRjYvUSgmbWludXM7RidGMkZDRklGS0ZNRk9GUUZTRlUvRlhRLDAuMjIyMjIyMmVtRicvRmVuRltyRmZuLUZpbjYlUSYwLjE2NEYnRjJGQ0YyRkBGQw==">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</Equation><Font encoding="UTF-8"> p\303\245 tilfredsstillende vis kan beskrive sammenh\303\246ngen mellem tiden og hastigheden.  </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Et v\303\246ksthus har hver anden dag i en lang periode plantet sm\303\245 bambusplanter. De har p\303\245 en bestemt dag m\303\245lt alle planternes h\303\270jde. Tabellen viser sammenh\303\246ngen mellem, hvor mange dage det er siden planten blev plantet og plantens h\303\270jde i cm.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">b) Vurder residualspredningen (fra residualplottet) ved at sammenligne residualspredning med y-v\303\246rdierne. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">c) Vurder om datas\303\246ttet kan beskrives vha. en line\303\246r model.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">N\303\245r vi udf\303\270rer et eksperiment, kan vi betragte det at m\303\245le en </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8">-v\303\246rdi til en bestemt </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8">-v\303\246rdi som et stokastisk eksperiment. Nogle gange f\303\245r vi en lidt for h\303\270j eller lav v\303\246rdi i forhold til gennemsnittet af rigtig mange m\303\245linger ved lige netop denne x-v\303\246rdi. Variationen kan enten skyldes m\303\245leusikkerhed eller naturlige variationer i det, som vi m\303\245ler p\303\245.
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">I nedenst\303\245ende figur symboliserer de gule prikker vores resultater, hvis vi havde m\303\245lt mange gange ved hver </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8">-v\303\246rdi. Men ofte m\303\245ler vi kun \303\251n gang, hvilket symboliseres ved de gr\303\270nne prikker.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Vi kan bruge et QQ-plot til at vurdere om residalerne er normalfordelte. I Maple benyttes kommandoen <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEvcmVzaWR1YWxRUXBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEvcmVzaWR1YWxRUXBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyL0Y2USdub3JtYWxGJw==</Equation> til at tegne et QQ-plot af residualerne. </Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Hvis QQ-plottet viser at residualerne ser ud til tiln\303\246rmelsesvist at f\303\270lge en normalfordeling, giver det en indikation af at den line\303\246re model passer godt til datas\303\246ttet. </Font></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" bold="false" layout="Heading 1"><Font bold="false" encoding="UTF-8">Opgave 2 - forts\303\246ttelse</Font></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">I opgave 2 regnede I p\303\245 et stort datas\303\246t omkring bambusplanters h\303\270jde som funktion af planternes alder.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">a) I skal nu afg\303\270re om residualerne er normalfordelte. Benyt f\303\270lgende kommando for QQplot af residualerne:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">b) Giv en vurdering af QQ-plottet. Er residualerne normalfordelte?</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">N\303\245r man skal vurdere, om et datas\303\246t kan beskrives ved hj\303\246lp af en line\303\246r model, er der netop tale om en vurdering, og svaret kan ikke altid gives entydigt. For at give en kvalificeret vurdering er det relevant at g\303\245 igennem en r\303\246kke punkter, som er vist nedenfor.</Font></Text-field>
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<Font bold="true">1)<Font encoding="UTF-8"> Tegn et punktplot af data, og lav line\303\246r regression.</Font></Font> </Text-field>
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<Input><Text-field style="Text" layout="Normal" bullet="dot"> Passer datapunkterne nogenlunde med regressionslinjen?</Text-field>
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<Input><Text-field style="Text" layout="Normal" bullet="dot"> Er forklaringsgraden <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGQQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGQQ==</Equation><Font encoding="UTF-8"> forholdsvis t\303\246t p\303\245 1?</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" bullet="dot"><Font encoding="UTF-8">Er residualerne tilf\303\246ldigt spredte, eller er der en systematik i residualernes placering</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" bullet="dot"><Font encoding="UTF-8">Er der enkelte af datapunkterne, som har residualer, der er langt st\303\270rre end residualspredningen (outlier)? Kan de skyldes en m\303\245lefejl?</Font></Text-field>
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<Font encoding="UTF-8">F\303\270lger residualerne i fraktilplottet en ret linje uden systematisk afvigelse?</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">d) Unders\303\270g om residualerne er normalfordelte.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">e) Vurder den line\303\246re models anvendelighed til at beskrive sammenh\303\246ngen.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi ved fra tidligere at residualerne fra datas\303\246ttet i eksempel 1 om bambush\303\270jder er normalfordelte: </Font></Text-field>
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<Input><Text-field style="Text" underline="true" layout="Normal"><Font underline="false">Benyt kommandoen <Font italic="true">residualspredning</Font>:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font underline="true" encoding="UTF-8">Middelv\303\246rdi for residualerne</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Middelv\303\246rdierne for residualerne kan ogs\303\245 bestemmes:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Residualerne kan tr\303\246kkes ud af datas\303\246ttet med kommandoen </Font><Font italic="true">residualer </Font><Font encoding="UTF-8">(her vises kun 5 af r\303\246kkerne):</Font>  </Text-field>
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<Input><Text-field style="Text" layout="Normal">Denne matrix har <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==</Equation><Font encoding="UTF-8">-v\303\246rdierne i f\303\270rste s\303\270jle og residualerne i anden s\303\270jle. Vi skal kun benytte residualerne i s\303\270jle 2. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Man f\303\245r fat i anden s\303\270jle i en matrix ved at skrive: (1..57 fordi man \303\270nsker alle r\303\246kker, men kun s\303\270jle 2) </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Og s\303\245 tager man middelv\303\246rdien af alle disse v\303\246rdier: </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnbWlkZGVsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEkcmVzRidGL0YyLUY2NiYtRiM2KS1JI21uR0YkNiRRIjFGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYuUSMuLkYnRkUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk0vJSlzdHJldGNoeUdGTS8lKnN5bW1ldHJpY0dGTS8lKGxhcmdlb3BHRk0vJS5tb3ZhYmxlbGltaXRzR0ZNLyUnYWNjZW50R0ZNLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRicvJSllcXVhbGl0eUdGTS1GQjYkUSM1N0YnRkUtRkg2LlEiLEYnRkVGSy9GT0YxRlBGUkZURlZGWC9GZW5GaW4vRmhuUSwwLjMzMzMzMzNlbUYnRmpuLUZCNiRRIjJGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFRkUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGaW9GRUZFRmlvRkU=">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</Equation> = </Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi f\303\245r alts\303\245 at middelv\303\246rdien for residualerne er 0 og spredningen er 24,5. </Font>R<Font encoding="UTF-8">esidualerne f\303\270lger dermed en normalfordeling med middelv\303\246rdi 0 og en spredning p\303\245 24,5. </Font>Dvs. <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">En tilf\303\246ldig bambus udv\303\246lges. Sandsynligheden for, at h\303\270jden p\303\245 denne bambus afviger mere end 25 cm fra modellen, kan nu bestemmes ud fra normalfordelingen: </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi skal have fat i sandsynligheden for, at residualerne bliver mindre end -25 og st\303\270rre end 25.  </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Dvs. vi f\303\245r en sandsynlighed p\303\245 </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">I  en model antager man, at der er en line\303\246r sammenh\303\246ng
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<Input><Text-field style="Text" layout="Normal"><Font size="16" bold="true" encoding="UTF-8">Konfidensinterval for h\303\246ldningskoefficienten</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi forestiller os, at man udf\303\270rer samme eksperiment to eller flere gange og dern\303\246st udf\303\270rer line\303\246r regression over resultaterne for at finde en line\303\246r model, som kan beskrive sammenh\303\246ngen mellem de indg\303\245ende variable. S\303\245 er det meget sandsynligt at m\303\245leresultaterne ikke vil blive helt ens og dermed vil regressionsmodellerne heller ikke blive helt ens. De vil sikkert v\303\246re t\303\246t p\303\245 hinanden men alts\303\245 ikke helt ens. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Det kunne v\303\246re meget interessant at vide noget om usikkerheden p\303\245 en models h\303\246ldningskoefficient. Dette kan vi benytte konfidensintervaller til at vurdere. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi skelner i denne forbindelse mellem den h\303\246ldningskoefficient, der er kommet ud af regressionen og s\303\245 den &quot;sande&quot; h\303\246ldningskoefficient. Vi kan ud fra datas\303\246ttet ved hj\303\246lp af v\303\246rkt\303\270jsprogrammer bestemme et konfidensinterval for h\303\246ldningen, dvs. et interval, hvori den sande h\303\246ldningskoefficient med 95 % sandsynlighed befinder sig.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">I Maple benytter vi kommandoen <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEodGVzdExpbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEodGVzdExpbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> til at bestemme dette konfidensinterval. </Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="Maple Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi udf\303\270rer line\303\246r regression hvor den uafh\303\246ngige variabel er dage siden plantning og den afh\303\246ngige er h\303\270jde i cm. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnTGluUmVnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEmZGF0YTFGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnTGluUmVnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEmZGF0YTFGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Forskriften for den line\303\246re model er </Font>y =<Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">. Dvs. h\303\246ldnigskoefficienten er 2,6261.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Vi vil nu benytte Maple-kommandoen <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEodGVzdExpbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEodGVzdExpbkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS8lKWVxdWFsaXR5R0YxRi9GMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS8lKWVxdWFsaXR5R0YxRi9GMg==</Equation><Font italic="true"> </Font><Font encoding="UTF-8">til at beregne 95%-konfidensinterval for h\303\246ldningstallet: </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Vi tager udgangspunkt i samme eksempel om en kugles fald, som vi arbejdede med tidligere:</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi ser bort fra en meget lav forklaringsgrad og antager at y-v\303\246rdierne afh\303\246nger line\303\246rt af x-v\303\246rdierne.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Udmiddelbart ser modellen voksende ud, da h\303\246ldnigskoefficienten er positiv. Den er dog med v\303\246rdien 0.18 meget lav. </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Her kan vi benytte konfidensintervallet til at udtale os om den sande h\303\246ldningskoefficient for sammenh\303\246ngen mellem de sammenh\303\270rende v\303\246rdier.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Vi laver en testLin p\303\245 dette datas\303\246t</Font></Text-field>
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