The regression lines will be perpendicular to each other if the coefficient of correlation $r$ is equal to.A. 1 onlyB. 1 or $ - 1$C. $ - 1$ onlyD. 0 Show
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Hint: If the two regression lines are completely correlated then the correlation coefficient is either -1 or 1. If the regression lines are not related then the correlation coefficient is given as 0.Complete step-by-step answer: Note: The regression line is a straight line that defines the change of a response variable $y$ as the independent variable $x$ changes. It is often used to predict the outcome $y$ on a new observation point $x$. Is the regression lines are perpendicular to each other the coefficient of correlation is?If the two regression lines are perpendicular to each other, there is no correlation between the two regression lines.
When the correlation coefficient r 0 then the two regression lines are?The regression line of y on x is y – y {bar} = 0 and regression line of x on y is x – x{bar} = 0. Hence the lines of regression are parallel to axes. Was this answer helpful?
When r =+ 1 or 1 the two regression lines?The two lines of regression coincide i.e. become identical when r = –1 or 1 or in other words, there is a perfect negative or positive correlation between the two variables under discussion.
When r is zero the regression line cut each other?Regression Lines:
If r = 0, i.e., both the variables are independent then the two lines will cut each other at right angle. In this case the two lines will be parallel to X and Y-axes.
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If the two lines of regression are perpendicular to each other the correlation coefficient r is
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