If the regression line of x on y is x - 4y = 5 then the regression coefficient of x on y is

  1. JEE Questions
  2. If The Lines Of Regression Of Y On X And That Of X On Y Are Y Kx 4 And X 4y 5

If the regression line of x on y is x - 4y = 5 then the regression coefficient of x on y is

1) k ≤ 0

2) k ≥ 0

3) 0 ≤ k ≤ 1 / 4

4) 0 ≤ k ≤ 1

Solution: (3) 0 ≤ k ≤ 1 / 4

m1m2 ≤ 1

k . 4 ≤ 1

k ≤ 1 / 4

Also, m1 and m2 must be of the same sign.

k ≥ 0

Hence 0 ≤ k ≤ 1 / 4

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if x is equal to 4 Y + fine and where is Dukh Express Pora the lines of regression or nationwide and Y on X respectively where is positive constant prove that it can take one line of regression of Y on X is given by Y is equal to X + 10 the line of origin of x on Y given by x is equal to four ok sunao general equation of a lower end of line of regression of Y on X is given by Y minus Y is equal to X

2 x minus 2 equations that Y is equal to b y x y x x we can say that the value of Y is equal to the equation of line of regression of X and Y is given by x minus 6 is equal to b h u

x x minus y again comparing the equation we can say that the value of x is equal to four ok sunao relation which is the product of V X Y and Z to put in the values we can say that ok is equal to cannot take need one cause I always like between -1 and 1

question we can say that focus on to be less than equal to 1

Given equations of regression lines are

x - 4y = 5           …(i)

16y - x = 64

i.e., - x + 16y = 64      …(ii)

Adding (i) and (ii), we get

   x - 4y = 5
- x + 16y = 64  
12y  =  69

∴ y = `69/12 = 5.75`

Substituting y = 5.75 in (i), we get

x - 4(5.75) = 5

∴ x - 23 = 5

∴ x = 5 + 23 = 28

Since the point of intersection of two regression lines is `(bar x, bar y)`,

∴ `bar x = 28  and bar y = 5.75`

Let, x - 4y = 5 be the regression equation of X on Y

∴ The equation becomes X = 4Y + 5

Comparing it with X = bXY Y + a', we get

bXY = 4

Now, the other equation i.e. 16y - x = 64 is regression equation of Y on X

∴ The equation becomes 16Y = X + 64

i.e., Y = `1/16 "X" + 64/16`

Comparing it with Y = bYX X + a, we get

`"b"_"YX" = 1/16`

r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt(4 xx 1/16) = +- sqrt(1/4) = +- 1/2 = +- 0.5`

Since bXY and bYX both are positive,

r is also positive.

∴ r = 0.5

How do you find the regression coefficient of X on Y?

The regression equation X on Y is X = c + dy is used to estimate value of X when Y is given and a, b, c and d are constant. Y = a + bx can also be interpreted as 'a' is the average value of Y when X is zero. X = c + dy, value c is the average value of X, when Y is zero.

What is the regression coefficient for X?

The regression coefficient of y on x is denoted by byx. The regression coefficient of x on y is denoted by bxy. 4.

Is regression X on Y or Y on X?

If y represents the dependent variable and x the independent variable, this relationship is described as the regression of y on x. The relationship can be represented by a simple equation called the regression equation.

What are the regression lines and coefficients of x and y variables?

Regression Coefficient The two constants a and b are regression parameters. Furthermore, we denote the variable b as byx and we term it as regression coefficient of y on x. Also, we can have one more definition for the regression line of y on x. We can call it the best fit as the result comes from least squares.