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Check the document that i attached, for more information
What I under stand from your question is that regression line of the form
Y and X are two variables . a,b are constant to be determined as.
solving system of equation (i) and (ii) for a,b. we can get regression line.
A linear equaton colud be compaeared as weights on a a scale, you know some weghts vaue, the weights "x" none
when we have i.e:
`7x +5 = x + 17`
the symbol "equal" means tha wheights on the left and right side are equivalents.
Now You can immagine the left side as sum of a known weight `5` and seven weights of value `x`
On the right side we have a weight of value `17` an only one weight of value: `x`
First step is to separate `x` weigts and know values keeping the equivalence. To do this we have , step by step, ad or subtract same weights.
In the example, if we take an x weights both sides, we get:
`7x + 5 - x = x + 17 - x`
subtracting by like terms:
`6x + 5=17`
You can see this operation allow us to have `x` weights only on lefs side .
But we havent separate `x` from known yet
To mange this we have to deed wit another subraciono taking away
the weight `5` from both sides, this in order to manage only `x` on the left side an known weight on the rigth side.
`6x +5 -5 =17 -5`
having subtract the weight `5` from both sidethe scale is still in the balance.
So operating with similar terms we get:
`6x = 12`
At once we know, if six equal weights acting as a weight of value
`12` only singe weights `x` act as `12/6` that is `2`
FIRST STEP: SEPARTING X VALUE FROM KNOW VALUE
SECOND STEP: IS DIVIDE KNOWN VALUE BY NUMBER OF `x` is on the other side of the scale.
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