Least Squares for Practitioners

Table 1

Estimation of quadratic polynomials for interpolation purposes.

Observations Used	Estimated quadratic polynomial
(1, 5)	${\widehat{p}}_1(x)=1.66667+1.66667x+1.66667x^2\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{near}\mathrm{\hspace{0.17em}\hspace{0.17em}}x=1$
(1, 5), (2, 7)	${\widehat{p}}_2(x)=3.00000+2.00000x+0.00000x^2\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{for}\mathrm{\hspace{0.17em}\hspace{0.17em}}x\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{in}\mathrm{\hspace{0.17em}\hspace{0.17em}}(\mathrm{1,2})$
(1, 5), (2, 7), (3, 13)	${\widehat{p}}_3(x)=7.00000-4.00000x+2.00000x^2\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{for}\mathrm{\hspace{0.17em}\hspace{0.17em}}x\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{in}\mathrm{\hspace{0.17em}\hspace{0.17em}}(\mathrm{1,3})$
(1, 5), (2, 7), (3, 13), (4, 8)	${\widehat{p}}_4(x)=-4.25000+10.25000x-1.75000x^2\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{for}\mathrm{\hspace{0.17em}\hspace{0.17em}}x\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{in}\mathrm{\hspace{0.17em}\hspace{0.17em}}(\mathrm{1,4})$
(1, 5), (2, 7), (3, 13), (4, 8), (5,6)	${\widehat{p}}_5(x)=-2.60000+8.44286x-1.35714x^2\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{for}\mathrm{\hspace{0.17em}\hspace{0.17em}}x\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{in}\mathrm{\hspace{0.17em}\hspace{0.17em}}(\mathrm{1,5})$