Two variables, x and y, have a correlation of 0.75. F x has a mean of 25 and a standard deviation of 3, and yy has a mean of 12 and a standard deviation of 6, what is the least-squares regression line for the two variables?

the least-squares regression line for the two variables

    y = 1.5x -25.5

Step-by-step explanation:

Explanation:-

Let the straight line satisfying the general trend of n dots in a scatter diagram

be y = a + b x   ... (1)

we have to determine the constants a and b so that (1) gives for each value of 'x' the best estimate for the average value of y in accordance with the principal of least squares

The normal equations of a and b are

∑y =n a +b∑ x

∑x y = a ∑x +b∑x^2

The line of best fit formula is

Now given data

mean of x is x⁻ = 25

standard deviation of x =3

mean of y is y⁻ = 12

standard deviation of y =6

Given Two variables, x and y, have a correlation of 0.75.

r=0.75

The equation of least squares best fit regression line is

on simplification we get y-12 = 1.5(x-25)

                                          y = 12 + 1.5x - 1.5X25

                                       y = 1.5x -25.5

lo98765432wqasdfghjkloi87654567890

step-by-step explanation: