Equations of two lines of regression are 4x+3y+7 = 0 and 3x+ 4y + 8 = 0, themean of x and y are(a) 5/7 and 6/7(b) – 4/7 and –11/7(c) 2 and 4(d) None of these
Question
Equations of two lines of regression are 4x+3y+7 = 0 and 3x+ 4y + 8 = 0, themean of x and y are(a) 5/7 and 6/7(b) – 4/7 and –11/7(c) 2 and 4(d) None of these
Solution
The equations of two lines of regression are given as 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0.
The mean of x and y can be found by solving these two equations simultaneously.
Step 1: Rewrite the equations in the form y = mx + c
For the first equation: 3y = -4x - 7, so y = -4/3x - 7/3
For the second equation: 4y = -3x - 8, so y = -3/4x - 2
Step 2: Solve the equations simultaneously
Set the two equations equal to each other and solve for x:
-4/3x - 7/3 = -3/4x - 2
Cross multiply to get rid of the fractions:
-16x - 28 = -9x - 6
Combine like terms:
7x = 22
So, x = 22/7 = 3.14
Substitute x = 3.14 into the first equation to solve for y:
y = -4/3(3.14) - 7/3 = -4.18 - 2.33 = -6.51
So, the mean of x is 3.14 and the mean of y is -6.51.
Therefore, the answer is not listed in the options given. So, the correct answer is (d) None of these.
Similar Questions
43.A linear regression line has an equation of the form Y = a + bX, what is X and Y? A. Where X is not the explanatory variable and Y is the dependent variable B. Where X is the explanatory variable and Y is the independent variable. C. Where X is the explanatory variable and Y is the dependent variable D. Where X and Y are the independent variable
Regression line equation is in which form of equation?a.intercept form of equationb.point slope form of equationc.two point form of equationd.no form of equation
4. The pair of equations y = 0 and y = -7 has
General equation of the regression line x on y is ________.a.(x-xbar)=b_xy (y-ybar)b.(x-xbar)=b_yx (y-ybar)c.(x+xbar)=b_xy (y+ybar)d.(y-ybar)=b_xy (x-xbar)
What is the y-intercept of the line described by the equation below?y = 7x + 4A.(0, -7)B.(0, -4)C.(0, 4)D.(0, 7)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.