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Problem: Quadratic fit {{1996,1997,1998,1999,2000},{40,50,62,58,60}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Quadratic fit {{1996,1997,1998,1999,2000},{40,50,62,58,60}}


The equation is `y = a + bx + cx^2` and the normal equations are

`sum y = an + b sum x + c sum x^2`

`sum xy = a sum x + b sum x^2 + c sum x^3`

`sum x^2y = a sum x^2 + b sum x^3 + c sum x^4`


`X``y``x = X - 1998``x^2``x^3``x^4``x*y``x^2*y`
199640-24-816-80160
199750-11-11-5050
199862000000
19995811115858
20006024816120240
------------------------
999027001003448508


Substituting these values in the normal equations
`270=5a+0b+10c`

`48=0a+10b+0c`

`508=10a+0b+34c`


Solving these 3 equations,
Total Equations are `3`

`5a+0b+10c=270 -> (1)`

`0a+10b+0c=48 -> (2)`

`10a+0b+34c=508 -> (3)`



Select the equations `(1)` and `(3)`, and eliminate the variable `a`.

`5a+10c=270`` xx 2->````10a``+``20c``=``540```
`10a+34c=508`` xx 1->````10a``+``34c``=``508```

`-``14c``=``32`` -> (4)`









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