Question

2. Estimate the regression equation from the following data.
X: 7 4 8 6 5
Y: 6 5 9 8 2
Also estimate the value of y when x=10.​

Answer 1

Given :

X: 7 4 8 6 5

Y: 6 5 9 8 2

To Find : Estimate the regression equation

estimate the value of y when x=10

Solution:

y = a + bx

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

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

 $\overline{x}=\dfrac{7+4+8+6+5}{5} =6$

$\overline{y}=\dfrac{ 6+5+9+8+2}{5} =6$

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

7 6 1 0 0 1  

4 5 -2 -1 2 4  

8 9 2 3 6 4  

6 8 0 2 0 0  

5 2 -1 -4 4 1    

                               12     10

b = 12/10 = 1.2

6 = a + 1.2(6)

=> a = - 1.2

y = -1.2 + 1.2x

or

y - 6  = 1.2(x - 6)

=> y = 1.2x  - 1.2

regression equation

x  = 10

=> y = 12 - 1.2  = 10.8

Value of y = 10.8 when x  = 10

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