Answer to Question #130888 in Statistics and Probability for lahon

Question #130888
https://www.chegg.com/homework-help/questions-and-answers/prob-2-data-collected-mass-kitten-kilograms-age-weeks-5-age-weeks-1-mass-kg-08-11-12-14-15-q36517894
1
Expert's answer
2020-08-27T17:05:00-0400

Data were collected on the mass of a kitten, in kilograms, and its age in weeks.


Age(weeks)1234567Mass(kg)0.81.11.21.41.51.51.7\def\arraystretch{1.5} \begin{array}{c: c: c: c:c: c: c: c} Age(weeks) & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline Mass(kg) & 0.8 & 1.1 & 1.2 & 1.4 & 1.5 & 1.5 & 1.7 \end{array}

n=7,ixi=28,xˉ=ixin=4n=7,\sum_ix_i=28, \bar{x}=\dfrac{\sum_ix_i}{n}=4

n=7,iyi=9.3,yˉ=ixin=9.27n=7,\sum_iy_i=9.3, \bar{y}=\dfrac{\sum_ix_i}{n}=\dfrac{9.2}{7}

Sxx=i(xixˉ)2=ixi2nxˉ2=S_{xx}=\sum_i(x_i-\bar{x})^2=\sum_ix_i^2-n\bar{x}^2==1407(4)2=28=140-7(4)^2=28

Syy=i(yiyˉ)2=iyi2nyˉ2=S_{yy}=\sum_i(y_i-\bar{y})^2=\sum_iy_i^2-n\bar{y}^2==12.647(9.27)2=0.548571=12.64-7(\dfrac{9.2}{7})^2=0.548571

Sxy=i(xixˉ)(yiyˉ)=ixiyinxˉyˉ=S_{xy}=\sum_i(x_i-\bar{x})(y_i-\bar{y})=\sum_ix_iy_i-n\bar{x}\bar{y}==40.67(4)(9.27)=3.8=40.6-7(4)(\dfrac{9.2}{7})=3.8

Therefore, based on the above calculations, the regression coefficients (the slope m,m,

and the y-intercept nn) are obtained as follows:


m=SSxySSxx=3.828=0.135714m=\dfrac{SS_{xy}}{SS_{xx}}=\dfrac{3.8}{28}=0.135714

n=yˉmxˉ=9.273.8284=5.470.771429n=\bar{y}-m\cdot\bar{x}=\dfrac{9.2}{7}-\dfrac{3.8}{28}\cdot 4=\dfrac{5.4}{7}\approx0.771429

Therefore, we find that the regression equation is:


y=0.771429+0.135714xy=0.771429+0.135714x


y(10)=0.771429+0.135714(10)=2.13(kg)y(10)=0.771429+0.135714(10)=2.13(kg)


r=SSxySSxxSSyyr=\dfrac{SS_{xy}}{\sqrt{SS_{xx}}\sqrt{SS_{yy}}}

r=3.8280.548571=0.9696r=\dfrac{3.8}{\sqrt{28}\sqrt{0.548571}}=0.9696

0.7<r10.7<r\leq1 strong correlation



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