Question

The fol table gives the normal weight of a baby dunng first six months of life. 1 2 3 4 5 Age (in Months)x) 8 7 Weight in 2 5 3 lbs.(Y) What would be the weight of the baby at the 6 month of life (HINT use Yua+bX) ,​

Answer 1

Given : normal weight of a baby during first six months of life

To Find : the weight of the baby at the 6 month of life

Solution:

y = a + bx

$y-\overline{y}=b(x-\overline{x})$

$b=\dfrac{\sum(x-\overline{x}).(y-\overline{y})}{\sum(x-\overline{x})^2}$

$\overline{x}=\dfrac{ 1+2+3+4+5}{5} =3$

$\overline{y}=\dfrac{ 2+3+5+7+8}{5} =5$

x        y    $x-\overline{x}$    $y-\overline{y}$     $(x-\overline{x}) (y-\overline{y})$    $(x-\overline{x})^2$

1 2 -2.00 -3.00 6.00 4.00

2 3 -1.00 -2.00 2.00 1.00

3 5 0.00 0.00 0.00 0.00

4 7 1.00        2.00        2.00    1.00

5 8 2.00 3.00 6.00 4.00

                  16.00 10.00

$b=\dfrac{\sum(x-\overline{x}).(y-\overline{y})}{\sum(x-\overline{x})^2}$

b = 16/10 = 1.6

Either use $\overline{y}=a+b\overline{x}$   to find a

=> 5 = a  + 1.6* 3  => a  =  0.2

y = 0.2 + 1.6x

or use $y-\overline{y}=b(x-\overline{x})$

=> y - 5 = 1.6(x - 3)

=> y - 5 = 1.6x - 4.8

=> y = 0.2 + 1.6x

y = 0.2 + 1.6x is  the least square regression line

a = 0.2 , b = 1.6

value of y when x = 6

=> y = 0.2 + 1.6 * 6 = 9.8

the weight of the baby at the 6 month of life    = 9.8  lb

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