Answer to Question #220932 in Statistics and Probability for Irfan

Question #220932
If you want to fit a linear regression line y=a+bx from the above data, then what is the value of 'a'?
1
Expert's answer
2021-07-28T06:50:00-0400
xˉ=ixin\bar{x}=\dfrac{\sum_ix_i}{n}

yˉ=iyin\bar{y}=\dfrac{\sum_iy_i}{n}

SSxx=i(xixˉ)2=ixi2n(xˉ)2SS_{xx}=\sum_i(x_i-\bar{x})^2=\sum_ix_i^2-n(\bar{x})^2

SSyy=i(yiyˉ)2=iyi2n(yˉ)2SS_{yy}=\sum_i(y_i-\bar{y})^2=\sum_iy_i^2-n(\bar{y})^2

SSxy=i(xixˉ)(yiyˉ)=ixiyinxˉyˉSS_{xy}=\sum_i(x_i-\bar{x})(y_i-\bar{y})=\sum_ix_iy_i-n\bar{x}\bar{y}

b=SSxySSxxb=\dfrac{SS_{xy}}{SS_{xx}}

a=yˉbxˉa=\bar{y}-b\bar{x}


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