Let $$\overline x $$ be the mean of x₁, x₂, x₃, ....., x_n. If x_i = a + cy_i for some constants a and c, then what will be the mean of y₁, y₂, y₃, ....., y_n ?

Consider the following statements

I. If the correlation coefficient r_xy = 0, then the two lines of regression are parallel to each other.

II. If the correlation coefficient r_xy = 1, then the two lines of regression are perpendicular to each other.

Which of the above statements is/are correct?

If 4x $$-$$ 5y + 33 = 0 and 20x $$-$$ 9y = 107 are two lines of regression, then what are the values of $$\overline x $$ and $$\overline y $$ respectively ?

Consider the following statements

I. Mean is independent of change in scale and change in origin.

II. Variance is independent of change in scale but not in origin.

Which of the above statements is/are correct?