Following are the two normal equations obtained fir deriving the regression line of y and x: 5a + 10b = 40 and 10a + 25b = 95. the regression line of y on x is given by
Answers
The normal equations obtained fir deriving the regression line of y and x: 5a + 10b = 40 and 10a + 25b = 95.
In order to find the regression line of y on x, we need to solve the 5a + 10b = 40 and 10a + 25b = 95 to find out the values of a and b. So, we have,
Given,
5a + 10b = 40 ...........(1)
10a + 25b = 95 .............(2)
2 × (1) gives,
10a + 20b = 80 ...........(3)
(2) - (3) gives,
10a + 25b = 95
10a + 20b = 80
----------------------
5b = 15
b = 3
from (1)
5a + 10b = 40
5a + 10 (3) = 40
5a + 30 = 40
5a = 40 - 30
5a = 10
a = 2
As, "a" represents the y-intercept and "b" represents the slope, so we have,
The regression line of y on x is given by Y = 2X + 3
y=2x+3
Step-by-step explanation:
Given,
5a + 10b = 40 ...........(1)
10a + 25b = 95 .............(2)
2 × (1) gives, we get
10a + 20b = 80 ...........(3)
(2) - (3) gives, we get
(10a + 25b) -(10a + 20b)= 95 - 80
10a + 25b - 10a - 20b = 15
5b = 15
b = 15/5 = 3
Put b = 3 in (1), we get
5a + 10b = 40
5a + 10 (3) = 40
5a + 30 = 40
5a = 40 - 30
5a = 10
a = 2
As, "a" represents the y-intercept and "b" represents the slope, so we have,
The regression line of y on x is given by Y = 2X + 3
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