If the correlation coefficient between the variables \(X\) and \(Y\) is zero, then the two lines of regression are
\(X=\overline{X}\) and \(Y=\overline{Y}\)
The regression coefficients are \(b_{yx}=r\frac{\sigma_y}{\sigma_x}\) and \(b_{xy}=r\frac{\sigma_x}{\sigma_y}\). When \(r=0\), both coefficients become zero, so the line of \(Y\) on \(X\) reduces to \(Y=\overline{Y}\) and the line of \(X\) on \(Y\) reduces to \(X=\overline{X}\), i.e. two lines parallel to the axes through the means.
Similar Questions
If the regression coefficient of x on y and y on x are \(- \frac{1}{2}\) and \(- \frac{1}{8}\) respectively, then what is the correlation coefficient between x and y?
For 10 observations on price (x) and supply (y), the following data was obtained:
∑x = 130, ∑y = 220, ∑ x 2= 2288, ∑y 2= 5506 and ∑ xy = 3467.
What is the line of regression of y on x?If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?
A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?
If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?
Consider the following statements:
1. The regression line of y on x is \(\rm y = \frac{3}{4}x+2\)
2. The regression line of x on y is \(\rm x = \frac{3}{4}y+\frac{1}{4}\)
Which of the above statements is/are correct?
Consider the following statements:
1. The coefficient of correlations r is \(\rm \frac{3}{4}\) .
2. The means of x and y are 3 and 4 respectively.
Which of the above statements is/are correct?
Let X and Y represent prices (in Rs) of a commodity in Kolkata and Mumbai respectively. It is given X̅ = 65, Y̅ = 67, σ X = 2.5, σ Y = 3.5 and r(X, Y) = 0.8. What is the equation of regression of Y on X ?
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?
If two variables X and Y are independent, then what is the correlation coefficient between them?
Important Questions from Correlation and Regression
If the regression coefficient of x on y and y on x are \(- \frac{1}{2}\) and \(- \frac{1}{8}\) respectively, then what is the correlation coefficient between x and y?
For 10 observations on price (x) and supply (y), the following data was obtained:
∑x = 130, ∑y = 220, ∑ x 2= 2288, ∑y 2= 5506 and ∑ xy = 3467.
What is the line of regression of y on x?If X 1, X 2, … X nis a simple random sample without replacement of size n from a finite population of N units with mean μ and variance σ 2, the covariance of (X i, Xj ) will be:
If x = X- \(\bar{X}\) and y = Y - \(\bar{Y}\) and the number of pairs (X, Y) is n, then the Karl Pearson's coefficient of correlation is:
The given table shows the ranking of ten students in two subjects mathematics and statistics.
Mathematics
Statistics
3
6
5
4
8
9
4
8
7
1
10
2
2
3
1
10
6
5
9
7
The coefficient of rank correlation is:
