From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]
which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]
and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]
where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]
Now, the variance S_xy is given by
