help to calculate the equations of least squares regression

Hello all..can someone help me with the following..please??

calculate y on x and x on y using
(i).using normal equation
(ii).using regression coefficients

what are the formula and difference between these two methods..??

arvin said:

Hello all..can someone help me with the following..please??

calculate y on x and x on y using
(i).using normal equation
(ii).using regression coefficients

what are the formula and difference between these two methods..??

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workings

Hello,please my working below for regression coefficients
i had calculate it using co-variance formula


sum x = 28, sum y = 29, sum x^2 = 146, sum y^2 = 175, sum x*y = 146, x mean = 4.66, y mean = 4.83

\(\displaystyle Sxy\, =\, \dfrac{\Sigma\, xy}{n}\, -\, \bar{x}\, \bar{y}\)

\(\displaystyle Sxx\, =\, \dfrac{\Sigma\, x^2}{n}\, -\, \bar{x}^2\)

\(\displaystyle Syy\, =\, \dfrac{\Sigma\, y^2}{n}\, -\, \bar{y}^2\)

Y mean = (sum y/n)
b = Sxy/Syy

a = (y mean) - (b*x mean)

d = Sxy/Syy
c = (x mean) - (d*y mean)

least squares regression lines Y on X
y = a + bx
y = 3.404 + 0.306x

least squares refression lines X on Y
x = c + dy
x = 3.18 + 0.306y

but am stuck on the normal eq but i guess simultaneous equation should be used