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| PAGE: 688 | SET: Exercises | PROBLEM: 78 |
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 xi yi)
(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 
.
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