1rBTX 06. ESTADÍSTICA/1.6.3 Bidimensional 1.6.3.33Q RectaRegFertilitzant Per tal d'estudiar l'efecte d'un fertilitzant, es compara la quantitat d'adob (X_i) amb la producció (Y_i) en cinc camps similars, amb els resultats següents:

X_i	Y_i
#x1	#y1
#x2	#y2
#x3	#y3
#x4	#y4
#x5	#y5

Arrodoneix als centèsims.
a) Calcula la mitjana de kg de fertilitzant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#7F007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»X«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

b) Calcula la mitjana de producció en tonelades «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»Y«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«/math»

d) Calcula el coeficient de correlació (Pearson) r

e) Determina l'equació y = mx+n de la recta de regressió?

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#G

]]> 1.0000000 0.3333333 0 0 a) X¯ =#Xb) Y¯= #Yc) σXY=#cd) r =#pe) equació =#e]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>70</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><mrow><mi>d1</mi><mo>*</mo><mi>d2</mi></mrow></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>+</mo><mi>Y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x4</mi><mo>,</mo><mi>y4</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x5</mi><mo>,</mo><mi>y5</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta_de_regressió</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>210</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>265</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>105</mn><mo>,</mo><mn>55</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>L</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>correlació</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>,</mo><mn>162</mn><mo>,</mo><mn>167</mn><mo>,</mo><mn>173</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>155</mn><mo>,</mo><mn>161</mn><mo>,</mo><mn>168</mn><mo>,</mo><mn>174</mn><mo>,</mo><mn>179</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168.4</mn><mo>,</mo><mn>167.4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi><mo>,</mo><mi>t5</mi></math></input><output><math 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wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo> </mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 20 40</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question>