Math, asked by camjanani8260, 1 month ago

2. The values ​​of y and their corresponding values ​​of y are shown in the table below 0 1 2 3 4 y 2 3 5 4 6 a) Find the least square regression line y = ax + bb) Estimate the value of y when x = 10. 5

Answers

Answered by amitnrw
3

Given : The values ​​of x and their corresponding values ​​of y

x  0 1 2 3 4

y 2 3 5 4 6  

To Find : least square regression line y = ax + b

Estimate the value of y when x = 10. 5

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{0+1+2+3+4}{5} =2

\overline{y}=\dfrac{ 2+3+4+5+6}{5} =4

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

0 2 -2    -2          4             4

1 3 -1    -1          1              1

2 4 0     0          0              0

3 5 1          1           1              1

4 6 2   2           4              4

           10             10

b = 10/10

=> b = 1

Either use

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

=> 4 = a  + 1* 2  => a  = 2

y = 2 + x

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

=> y - 4 = 1(x - 2)

=> y - 4 = x - 2

=> y = 2 + x

y = 2 + x is  the least square regression line

a = 2  , b = 1

value of y when x = 10. 5

=> y = 2 + 10.5 = 12.5

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Answered by jamwalanish120
1

Answer:11.65

Step-by-step explanation:we have used linear regression there.

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