Find the equation of the least squares regression line if x-bar = 20, s_x = 2, y-bar = 10, s_y = 4, r = 0.2?

Solution:

\(\overline{x}\) = 20

s_x = 2

\(\overline{y}\) = 10

s_y = 4

r = 0.2

The general equation of least squares regression line is

\(\widehat{y}\) = a + bx …… (1)

Where b = \(r\frac{s_{y}}{s_{x}}\)

a = \(\overline{y} - b\overline{x}\)

To determine a and b values, substitute the given values in the formula

b = \(r\frac{s_{y}}{s_{x}}\)

b = (0.2) 4/ 2

b = 0.4

So we get

a = \(\overline{y} - b\overline{x}\)

a = 10 - (0.4) (20)

a = 10 + 8

a = 18

Substitute a and b values in (1)

\(\widehat{y}\) = 18 + 0.4x

You may also try the regression line calculator, here.

Therefore, the equation is \(\widehat{y}\) = 18 + 0.4x

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Find the equation of the least squares regression line if x-bar = 20, s_x = 2, y-bar = 10, s_y = 4, r = 0.2?

Summary:

The equation of the least squares regression line if x-bar = 20, sx = 2, y-bar = 10, sy = 4, r = 0.2 is \(\widehat{y}\) = 25.36 - 1.68x.