Answer to Question #160382 in Statistics and Probability for Abu Ubayda

Question #160382

Find the regression line of y on x for the following data:


X 40 70 50 60 80 50 90 40 60 60


Y 2.5 6.0 4.5 5.0 4.5 2.0 5.5 3.0 4.5 3.0


Draw the line. Estimate the value of y when x = 10.


1
Expert's answer
2021-02-03T03:52:49-0500
xˉ=60010=60,yˉ=40.510=4.05\bar{x}=\dfrac{600}{10}=60, \bar{y}=\dfrac{40.5}{10}=4.05


SSxx=xi2nxˉ2=2400SS_{xx}=\sum x_i^2-n\bar{x}^2=2400

SSyy=yi2nyˉ2=16.225SS_{yy}=\sum y_i^2-n\bar{y}^2=16.225

SSxy=xiyinxˉyˉ=140SS_{xy}=\sum x_iy_i-n\bar{x}\bar{y}=140

b=SSxySSxx=1402400=7120=0.0583b=\dfrac{SS_{xy}}{SS_{xx}}=\dfrac{140}{2400}=\dfrac{7}{120}=0.0583

a=yˉbxˉ=4.057120(60)=0.55a=\bar{y}-b\bar{x}=4.05-\dfrac{7}{120}(60)=0.55

Y=a+bXY=a+bX

Y=0.55+0.0583XY=0.55+0.0583X


r=SSxySSxxSyy=140240016.225=0.7095r=\dfrac{SS_{xy}}{\sqrt{SS_{xx}}\sqrt{S_{yy}}}=\dfrac{140}{\sqrt{2400}\sqrt{16.225}}=0.7095

r2=0.5033r^2=0.5033

Moderate positive correlation.


X=10X=10


Y=0.55+0.0583(10)=1.133Y=0.55+0.0583(10)=1.133




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