The equation of least squares regression parabola is .

The system of equations are

                       (Equation 1)

      (Equation 2)

   (Equation 3)

Observe the graph, the 5 points

are lie on the line graph, so n = 5.

                                (Expand of )

                               (Substitute values of x - coordinates)                                    (Expand of )

                                   (Substitute values of y - coordinates)

                       (Expand of )

                               (Substitute values of square of x - coordinates)                   (Expand of )

                         (Substitute values of cube of x - coordinates)                   (Expand of )

                     (Substitute values of fourth root of x - coordinates)

     (Expand of )

                    (Substitute values of x_i y_i)

  (Expand of )

                   (Substitute values of )

The above values are substitute in system of equations as follows:

Rewrite the system of linear equations and interchange the equations 2 and 3 as follows:                                                       (Equation 1)

                                                   (Equation 2)

                                                             (Equation 3)

Adding negative two times the first equation to the second equation produces a new second equation.

So, the new system of equations are

                                                        (Equation 1)

                                                                (Equation 2)

                                                              (Equation 3)

Multiplying the second equation by produces a new second equation and multiplying the third equation by produces a new third equation.

So, the new system of equations are

                                                        (Equation 1)

                                                                  (Equation 2)

                                                                  (Equation 3)

The value of substitute in either equation 1, solve for c as follows:

                                                        (Write equation 1)

                                                  (Substitute )

                                                        (Subtract from each side)

                                                              (Apply LCM rule: )

                                                                 (Divide each side by 5)

So, the equation of least squares regression parabola is .

The equation of least squares regression parabola is .