CORRELACIÓN LINEAL

S E N O S B R I N D A L A S I G U I E N T E I N F O R M A C I Ó N P A R A P O D E R G R A F I C A R L A I N V E R S I Ó N Q U E S E H A C E E N P U B L I C I D A D P A R A L A V E N T A D E C I E R T O P R O D U C T O E N E L C U A L “ X ” R E P R E S E N T A L A I N V E R S I Ó N Y “ Y ” E L I N C R E M E N T O E L L A S V E N T A S F A C T U R A D A S .

x y1 1509.5 36.62 1539.3 38.53 1563.5 374 1599.2 36.25 1617.2 406 1654.5 42.37 1671.1 44.68 1671.2 44.49 1706.8 44.3

10 1720.1 44.311 1730.2 43.412 1754.4 44.113 1793.5 42.814 1802.9 40.915 1819.9 41.616 1848.1 43.717 1885.2 42.618 1924.5 43.619 1961.9 46.920 1983.5 45.3

suma 34756.5 843.1

De acuerdo a estos datos podemos decir que la grafica podría tener una correlación lineal continua ya que los datos solo incrementan poco a poco conforme pasan las semanas.

G R A F I C A D O S L O S VA L O R E S D E “ X ” Y “ Y ” E S TA S E V E R Í A D E E S TA M A N E R A .

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E N S E G U I D A S E E L E V A N A L C U A D R A D O L O S V A L O R E S D E “ X ” A L I G U A L Q U E L O S V A L O R E S D E “ Y ” , Y L U E G O D E B E M O S M U L T I P L I C A R L O S V A L O R E S D E “ X ” Y “ Y ” . D E S P U É S S E S A C A L A S U M A T O R I A D E C A D A C O L U M N A P A R A P O D E R S A C A R L A C O R R E L A C I Ó N L I N E A L .

x y x^2 y^2 xy1 1509.5 36.6 2278590.25 1339.56 55247.72 1539.3 38.5 2369444.49 1482.25 59263.053 1563.5 37 2444532.25 1369 57849.54 1599.2 36.2 2557440.64 1310.44 57891.045 1617.2 40 2615335.84 1600 646886 1654.5 42.3 2737370.25 1789.29 69985.357 1671.1 44.6 2792575.21 1989.16 74531.068 1671.2 44.4 2792909.44 1971.36 74201.289 1706.8 44.3 2913166.24 1962.49 75611.24

10 1720.1 44.3 2958744.01 1962.49 76200.4311 1730.2 43.4 2993592.04 1883.56 75090.6812 1754.4 44.1 3077919.36 1944.81 77369.0413 1793.5 42.8 3216642.25 1831.84 76761.814 1802.9 40.9 3250448.41 1672.81 73738.6115 1819.9 41.6 3312036.01 1730.56 75707.8416 1848.1 43.7 3415473.61 1909.69 80761.9717 1885.2 42.6 3553979.04 1814.76 80309.5218 1924.5 43.6 3703700.25 1900.96 83908.219 1961.9 46.9 3849051.61 2199.61 92013.1120 1983.5 45.3 3934272.25 2052.09 89852.55

suma 34756.5 843.1 60767223.45 35716.73 1470981.97

E N S E G U I D A S E S U S T I T U Y E N L O S VA L O R E S D E L A S S U M A T O R I A S E N L A S E C U A C I O N E S PA R A P O D E R O B T E N E R L A C O R R E L A C I Ó N .

SCx=Σx^2-((Σx)^2/n) 366508.837 0.725166879

SCy=Σy^2-((Σy)^2/n) 175.8495 r²= 0.525867002

SCxy=Σxy-((Σx*Σy)/n) 5821.7125

r=SCxy/√SCx*SCy

LU E G O Q U E YA S E H A N R E A L I Z A D O L A S F O R M U L A S A N T E R I O R E S , C O N D I C H O S VA L O R E S O B T E N I D O S S E R E A L I Z A U N A N U E VA S U S T I T U C I Ó N E N L A S F O R M U L A S PA R A S A C A R E L VA L O R D E A ₀ Y A ₁ C O M O S E M U E S T R A A C O N T I N U A C I Ó N.

a₀=Σx²*Σy-Σx*Σxy/n*Σx²-(Σx)² 14.5509793

a₁=n*Σxy-Σx*Σy/n*Σx²-(Σx)² 0.01588423

O B T E N I D O S E S T O S N U E V O S R E S U L T A D O S S E S U S T I T U Y E N U E V A M E N T E E N L A F O R M U L A Y = A ₁ X + A ₀ P A R A P O D E R O B T E N E R E L N U E V O V A L O R D E Y Q U E N O S I N D I C A R A L A C O R R E L A C I Ó N L I N E A L .

x y x^2 y^2 xy y=a₁x+a₀1 1509.5 36.6 2278590.25 1339.56 55247.7 38.528232052 1539.3 38.5 2369444.49 1482.25 59263.05 39.001582253 1563.5 37 2444532.25 1369 57849.5 39.385980744 1599.2 36.2 2557440.64 1310.44 57891.04 39.953047925 1617.2 40 2615335.84 1600 64688 40.238964156 1654.5 42.3 2737370.25 1789.29 69985.35 40.831446127 1671.1 44.6 2792575.21 1989.16 74531.06 41.095124428 1671.2 44.4 2792909.44 1971.36 74201.28 41.096712849 1706.8 44.3 2913166.24 1962.49 75611.24 41.66219161

10 1720.1 44.3 2958744.01 1962.49 76200.43 41.8734519311 1730.2 43.4 2993592.04 1883.56 75090.68 42.0338827112 1754.4 44.1 3077919.36 1944.81 77369.04 42.4182811913 1793.5 42.8 3216642.25 1831.84 76761.8 43.0393547814 1802.9 40.9 3250448.41 1672.81 73738.61 43.1886665915 1819.9 41.6 3312036.01 1730.56 75707.84 43.4586985916 1848.1 43.7 3415473.61 1909.69 80761.97 43.9066340117 1885.2 42.6 3553979.04 1814.76 80309.52 44.4959391318 1924.5 43.6 3703700.25 1900.96 83908.2 45.1201895719 1961.9 46.9 3849051.61 2199.61 92013.11 45.7142599520 1983.5 45.3 3934272.25 2052.09 89852.55 46.05735943

suma 34756.5 843.1 60767223.45 35716.73 1470981.97

Y A L G R A F I C A R N U E VA M E N T E L O S VA L O R E E S T O S S E V E R Á N D E L A S I G U I E N T E M A N E R A ( L O S N U E V O S VA L O R E S S E D E F I N I R Á N P O R L O S P U N T O S E N C O L O R R O J O .

Y A L M O M E N T O P O D E M O S O B S E R VA R Q U E R E A L M E N T E E X I S T E U N A C O R R E L A C I Ó N L I N E A L E N F O R M A A S C E N D E N T E .

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D E S PU É S D E E S T O H AY Q U E S A C A R E L E R R O R E S TÁ N D A R Y S U S T I T U I M O S N U E VA M E N T E L O S VA L O R E S E N L A F O R M U L A PA R A P O D E R D E T E R M I N A R E S T E .

S y/x=√(Σy²-a₀Σy-a₁Σxy)/n-2 0.50728048error estandar=