The estimate of b̂ in the following regression model Yi = α + βXi + ei is given by :
1
\(\hat{b}=\frac{\Sigma\left(\mathrm{X}_i-\overline{\mathrm{X}}\right)\left(\mathrm{Y}_i-\overline{\mathrm{Y}}\right)}{\Sigma\left(\mathrm{X}_i-\overline{\mathrm{X}}\right)^2}\)
2
b̂ = Y̅ - \(\hat{\alpha }\)X̅
3
\(\hat{b}=\frac{\Sigma\left(\mathrm{X}_i-\overline{\mathrm{X}}\right)\left(\mathrm{Y}_i-\overline{\mathrm{Y}}\right)}{\sqrt{\Sigma\left(\mathrm{X}_i-\overline{\mathrm{X}}\right)}}\)
4
\(\hat{b}=\frac{\Sigma\left(\mathrm{X}_i-\overline{\mathrm{X}}\right)^2}{\Sigma\left(\mathrm{Y}_i-\overline{\mathrm{Y}}\right)^2}\)