hello everyone restart the question how the question is that the equations of two regression line one line is what 13 x minus 3 Y + 7 = 20 and another line is what weight minus y minus 1 equals to zero now we have to find the ratio between mean of y series and mean of X rays ok now these are the options we have to verify which of the correct what are the Jeevan regression lines are given line what are the line that is this line hostess and S is this line ok now writing these two line lines are 13 1 - 3 Y + 11 = 20 this is the first time and what is another line this is minus y minus 1
equals to zero this is another you can see hear this one line and this is another time now we have to find the intersection point of these two lines we know that the intersection point of two regression lines give the mean value now we are to find this intersection point of this two line hair after shaving this two line ok now we're what the line the lines are again writing this is 13 1 - 10 Y + 11 = 20 and the second line is what us minus y minus 1 equal to zero now multiplying second equation by 10 we have what we can get second equation entertain that is 2 x minus y minus 1 equals to zero where to write this by
10 then what will we get we will get writing this two line again now we get this is what this is 13 - 10 Y + 7 = 20 and this land becomes what this is 20 - 10 Y - of 10 = 20 ok now after resolving this two lines we can get this will be minus this is minus plus and this is this is - OK then we can get what we can get here like 13 1 - 28 that is - of 7x and this is my minor cancel out and this is just the that means the 21 = 20 ok now for the solving this week and get the
value of that is 7 x is equals to minus 21 this is - - - cancel out then 1 vehicle what 7321 equals to 3 equals to what mean value that is equals to the mean value of 1 and what is the meaning of why that is the value of Y that is why goes to word from the above equation we can get here to 1 minus y minus 1 equals to zero then why goes to work that is 28 - 1 from the second line then this will be compared to into a text that is 3 minus one that is 32 the sick man on that is equals to 5 ok now why coast what this is 5 this is equals to Viber hence
this is mean by Y this is also me and my wife now we have to find what we have to find the ratio of Vice City to mean of factories that means we were upon Ek Bar then we can simply write this as Viber ratio ratio Viber upon Ek Bar that is equal to what is that is equal to 5 and what is that is equal to 3 and this is a required and Y 12 point Ek Bar equals to 5 by 3 now matching the option bye-bye Shri now let's Mein option this is 5 by 3 that means taken option is the correct option this is 5 by 3 option that is the answer is the right answer thank you
For the two regression equations 4y = 9x + 15 and 25x = 6y + 7 find correlation coefficient r, `barx, bary`
Solution
Given equations of regression lines are
4y = 9x + 15 and 25x = 6y + 7
y = `9/4x + 15/4` and y = `25/6x - 7/6`
`9/4x + 15/4 and y = 25/6x - 7/6`
`|9/4| < |25/6|`
bxy = `9/4. 1/(b_xy) = 25/6`
bxy = `9/4. b_xy = 6/25`
r = `sqrt(b_xy xx b_yx)`
= `sqrt(6/25 xx 9/4)`
= `sqrt90.54)`
r = ± 0.7348
r = 0.7348 ............(bxy, byx > 0)
Solving equations of regressions lines
`barx = 118/46 . bary = 438/46`
Notes
Given equation of regression lines are
4y = 9x + 15 and 25x = 6y + 7
y = `9/4x + 15/4` and y = `25/6x -7/6`
`9/4x + 15/4`
Concept: Regression Coefficient of X on Y and Y on X
Is there an error in this question or solution?
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We assume that 2x + 3y - 6 = 0 to be the line of regression of y on x.
2x + 3y - 6 = 0
⇒ `x = - 3/2y + 3`
⇒ `"bxy" = - 3/2`
5x + 7y - 12 = 0 to be the line of regression of x on y.
5x + 7y - 12 = 0
⇒ `y = - 5/7x + 12/7`
⇒ `"byx" = - 5/7`
Now,
r = `sqrt("bxy.byx") = sqrt(15/14)`
byx = `(rσ_y)/(σ_x) = - 5/7, "bxy" = (rσ_x)/(σ_y) = - 3/2`
⇒ `(σ_x^2)/(σ_y^2) = (3/2)/(5/7)`
⇒ `(σ_x^2)/(σ_y^2) = 21/10`
⇒ `(σ_x)/(σ_y) = sqrt(21/10)`.
For the variables x and y, the two regression lines are 6x + y = 30 and 3x + 2y = 25. What are the values of x̅, y̅ and r respectively?
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NDA (Held On: 17 Nov 2019) Maths Previous Year paper
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- \(\frac{{20}}{3},\frac{{35}}{9},\; - 0.5\)
- \(\frac{{20}}{3},\frac{{35}}{9},\;0.5\)
- \(\frac{{35}}{9},\frac{{20}}{3},\; - 0.5\)
- \(\frac{{35}}{9},\frac{{20}}{3},\;0.5\)
Answer (Detailed Solution Below)
Option 3 : \(\frac{{35}}{9},\frac{{20}}{3},\; - 0.5\)
Free
Electric charges and coulomb's law (Basic)
10 Questions 10 Marks 10 Mins
Concept:
The line of regression of y on x is given by: \(y - \;\bar y = {b_{yx}}\;\left( {x - \;\bar x} \right)\) where byx is called the regression coefficient of y on x.
Similarly, the line of regression of x on y is given by: \(x - \;\bar x = {b_{xy}}\;\left( {y - \bar y} \right)\) wherebxy is called the regression coefficient of x on y.
The correlation coefficient r2 = byx × bxy
The two lines of regression intersect each other at \(\left( {\bar x\;,\;\bar y} \right)\)
Calculation:
Given: Two regression lines are 6x + y = 30 and 3x + 2y = 25.
As we know that, the two lines of regression intersect each other at \(\left( {\bar x\;,\;\bar y} \right)\)
By solving these two equations: 6x + y = 30 and 3x + 2y = 25
We get \(\left( {\bar x\;,\;\bar y} \right) = \left( {\frac{{35}}{9},\frac{{20}}{3}} \right)\)
We can write 6x + y = 30 as line of regression of x on y: \(x - \frac{{35}}{9} = \; - \frac{1}{6} \times \left( {y - \frac{{20}}{3}} \right)\) ------(1)
By comparing equation (1), with line of regression of x on y which is given by: \(x - \;\bar x = {b_{xy}}\;\left( {y - \bar y} \right)\) we get \({b_{xy}} = \; - \frac{1}{6}\)
Similarly, we can write 3x + 2y = 25 as line of regression of y on x: \(y - \frac{{20}}{3} = \; - \frac{3}{2}\;\left( {y - \frac{{35}}{9}} \right)\) ------(2)
By comparing equation (2), with line of regression of x on y which is given by \(\;y - \;\bar y = {b_{yx}}\;\left( {x - \;\bar x} \right)\): we get \({b_{yx}} = \; - \frac{3}{2}\)
As we know that, r2 = byx × bxy
\( \Rightarrow {r^2} = \; - \frac{1}{6} \times \; - \frac{3}{2} = \frac{1}{4}\)
\( \Rightarrow r = \; \pm \frac{1}{2} = \; \pm 0.5\)
As we know that, sign of \(r,\;{b_{xy}}\;and\;{b_{yx}}\;is\;always\;same\)
⇒ r = - 0.5
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