Data were collected on the mass of a kitten, in kilograms, and its age in weeks.
Age(weeks)Mass(kg)10.821.131.241.451.561.571.7
n=7,∑ixi=28,xˉ=n∑ixi=4
n=7,∑iyi=9.3,yˉ=n∑ixi=79.2
Sxx=∑i(xi−xˉ)2=∑ixi2−nxˉ2==140−7(4)2=28
Syy=∑i(yi−yˉ)2=∑iyi2−nyˉ2==12.64−7(79.2)2=0.548571
Sxy=∑i(xi−xˉ)(yi−yˉ)=∑ixiyi−nxˉyˉ==40.6−7(4)(79.2)=3.8Therefore, based on the above calculations, the regression coefficients (the slope m,
and the y-intercept n) are obtained as follows:
m=SSxxSSxy=283.8=0.135714
n=yˉ−m⋅xˉ=79.2−283.8⋅4=75.4≈0.771429 Therefore, we find that the regression equation is:
y=0.771429+0.135714x
y(10)=0.771429+0.135714(10)=2.13(kg)
r=SSxxSSyySSxy
r=280.5485713.8=0.9696 0.7<r≤1 strong correlation
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