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In case of perfect correlation between x...

In case of perfect correlation between x and y, the number of regression lines is ……………..

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To solve the question regarding the number of regression lines in the case of perfect correlation between x and y, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Perfect Correlation**: - Perfect correlation occurs when the correlation coefficient \( r \) is either 1 or -1. This indicates a perfect positive or perfect negative linear relationship between the variables x and y. 2. **Identifying Regression Lines**: - In statistics, there are two regression lines: the regression line of y on x (denoted as \( y = a + bx \)) and the regression line of x on y (denoted as \( x = c + dy \)). 3. **Behavior of Regression Lines in Perfect Correlation**: - When there is perfect correlation, both regression lines will coincide. This means that they will overlap completely, and there will be no distinction between the two lines. 4. **Conclusion**: - Since both regression lines coincide, we conclude that there is effectively only one regression line in the case of perfect correlation. Thus, the number of regression lines in the case of perfect correlation between x and y is **one**.
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Knowledge Check

  • The correlation between X and a-X is

    A
    `-1`
    B
    `-(1)/(2)`
    C
    `-(1)/(4)`
    D
    0

  • Angle between the two lines of regression is given by

    A
    `tan^(-1){(b_(YX)-(1)/(b_(XY)))/(1+(b_(XY))/(b_(YX)))}`
    B
    `tan^(-1){(b_(YX)b_(XY)-1)/(b_(YX)+b_(XY))}`
    C
    `tan^(-1){(b_(YX)-b_(XY))/(1+b_(YX).b_(XY))}`
    D
    none of these

  • Find the value of the covariance between x and y , if the regression coefficient of y on x is 3.75 and sigma_x =2, sigma_y =8

    A
    7
    B
    30
    C
    15
    D
    1.875

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