Professor Vipin 2015
Interpolation and Extrapolation
Meaning
Suppose that data with x between 0 and 10 is used to produce a regression line y = 2x + 5. We can use
this line of best fit to estimate the y value corresponding to x = 6. Simply plug this value into our
equation and we see that y = 2(6) + 5 =17. Because our x value is among the range of values used to
make the line of best fit, this is an example of interpolation. Suppose as before that data with x between
0 and 10 is used to produce a regression line y = 2x + 5. We can use this line of best fit to estimate the y
value corresponding to x = 20. Simply plug this value into our equation and we see that y = 2(20) + 5 =45.
Because our x value is not among the range of values used to make the line of best fit, this is an example
of extrapolation.
Methods of Interpolation
The methods are as follows:
a) Graphic Method
b) Algebraic Method (most commonly used)
Binomial Expansion
a) Find the number of known values of ‘y’. Let us say there are ‘n’ known values of ‘y’
b) Take
c) Expand the left hand side of the equation using the binomial expansion, but take the exponsents
of ‘y’ as the subscripts.
d) Substitute the given values in the equation.
e) Solve the equation for the unknown.
Expansion
Equation to be Taken
(y-1)2
y2-2y1+y0=0
(y-1)3
y3-3y2+3y1=0
(y-1)4
y4-4y3+6y2-4y1+y0=0
(y-1)5
y5-5y4+10y3-10y2+5y1-y0=0
(y-1)6
y6-6y5+15y4-20y3+15y2-6y1+y0=0
(y-1)7
y7-7y6+21y5-35y4+35y3-21y2+7y1=0
(y-1)8
y8- 8y7+28y6- 56y5+70y4-56y3+28y2-8y1+y0
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