h. The following sample observations were randomly selected.
X 4 5 3 6 10
Y 4 6 5 7 7
Determine the regression equation.
"\\sum_iX_iY_i=173,\\sum_iX_i=186, \\sum_iY_i=175""\\bar{X}=\\dfrac{1}{n}\\sum_iX_i=\\dfrac{28}{5}=5.6"
"\\bar{Y}=\\dfrac{1}{n}\\sum_iY_i=\\dfrac{29}{5}=5.8"
"SS_{XX}=\\sum_iX_i^2-\\dfrac{1}{n}(\\sum_iX_i)^2=100-\\dfrac{(28)^2}{5}"
"=29.2"
"SS_{YY}=\\sum_iY_i^2-\\dfrac{1}{n}(\\sum_iY_i)^2=175-\\dfrac{(29)^2}{5}"
"=6.8"
"SS_{XY}=\\sum_iX_iY_i-\\dfrac{1}{n}(\\sum_iX_i)(\\sum_iY_i)"
"=173-\\dfrac{28(29)}{5}=10.6"
"m=slope=\\dfrac{SS_{XY}}{SS_{XX}}"
"=\\dfrac{10.6}{29.2}=0.3630137"
"n=\\bar{Y}-m\\bar{X}"
"=5.8-0.3630137(5.6)"
"=3.7671233"
Therefore, we find that the regression equation is:
Correlation coefficient:
"=0.752246"
Strong positive correlation.
Comments
Leave a comment