The following coordinate pairs are data that have been colle

The following coordinate pairs are data that have been collected. Calculate by hand the least squares polynomial function, g(x), representing the data for these eases: g(x) = a_0 (Constant term only) g(x) = a_o + a_1 x (Ordinary line) g(x) = a_1x + a_3x^3 g(x) = a_0 + a_2X^2 Data in coordinate pairs: (1, 3) (3, 6) (5, 8) (8, 9) (10, 8)

Solution

g(x) representing the above data :

plug in value of the co-ordinates in the function

(1,3) in the first function is a0 only since constant

(1,3) in the second function is a0 +a1 .

(1,3) in the third function is a1+a3

(1,3) in the fourth function is a0+a2

(3,6)   in the first function is a0

(3,6)   in the second function is a0+a1.1 plugging thevalues

(3,6)   in the third function is 3a1 +27a3 plugging thevalues

(3,6)   in the fourth function is a0+9a2 plugging thevalues

(5,8) in the first function is a0 only since constant.

(5,8) in the second function is a0+5a1

(5,8) in the third function is 5a1 +125a3

(5,8) in the fourth function is a0+25a2

(8,9) in the first function is a0

(8,9) in the second function is a0+8a1

(8,9) in the third function is 8a1+512a2

(8,9) in the fourth function isa0+64a2