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?
It is given that X̅ = 10, Y̅ = 90, σ X= 3, σ Y= 12 and r XY = 0.8. The regression equation of X on Y is
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?
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?
Variable Y regresses with variable X with the conditions that \(\overline X = 5.50\) , \(\overline Y = 3.50\) and b = 1.50 in the linear regression model (Y = a + bX), where \(\overline Y\) and \(\overline X\) are means of the respective variables and b refers to gradient of line of Y w. r. t X. Which one of the following values of parameter 'a' of the model is correct?
It is given that X̅ = 10, Y̅ = 90, σ X= 3, σ Y= 12 and r XY = 0.8. The regression equation of X on Y is
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, in a series. there are m items whose ranks are common, then which factor is added for correction for each repeating value in both the series?
