# showing on a scatterplot part of a set of collected data. An equation for the curve of best fit is y=1/4x^2-2x-3. How to determind proper data point in the set. (-6,18), (-2.5, 5), (9.0,-2.5),...

showing on a scatterplot part of a set of collected data. An equation for the curve of best fit is y=1/4x^2-2x-3. How to determind proper data point in the set.

(-6,18), (-2.5, 5), (9.0,-2.5), (3,-6), (6,-6), (12,9)(15,23)

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fitin curve is
y=(1/4)x^2-2x-3.
How to determind proper data point in the set ?
(-6,18), (-2.5, 5), (9.0,-2.5), (3,-6), (6,-6), (12,9)(15,23)
substitute x in fitted curve and calculate y . If calculated
y is near to the given y then that is proper data point.
let
x=6
y= (1/4).(6)^2- 2.6-3
y=9-15
y=-6
It is same as given value.
(6,-6) is proper data point.

Let regression line is
y= a +bx (i)
sum(y)= n. a+ b sum(x) (ii)
sum(xy) =a. sum(x)+ b sum(x^2) (iii)
n=7
sum(x)=36.5
sum(y)=40.5
sum(xy)=256
sum(x^2)=537.25
Thus equation reduces to
40.5=7a+36.5b (iv)
256=36.5a+537.25b (v)
solving (iv) and (v) for a and b , we have
a=5.113
b=.129
Thus best fitted line is
Y= 5.113+ .129 X