Given that; Sigma*x = 52; n = 8; Sigma*y = 225; Sigma*xy = 1335; Sigma * x ^ 2 = 380; Sigma * y ^ 2 = 7007 and Calculated the least squares regression line of y on x in form of y = a + bx
To find the least squares regression line of y on x in the form of y = a + bx, we need to calculate the values of a and b.
First, calculate the values required for the formulas:
Σx = 52 (given)
n = 8 (given)
Σy = 225 (given)
Σxy = 1335 (given)
Σx^2 = 380 (given)
Σy^2 = 7007 (given)
Next, use the formulas to calculate the values of a and b:
b = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
a = (Σy - bΣx) / n
Substitute the given values into the formulas:
b = (8 * 1335 - 52 * 225) / (8 * 380 - (52)^2)
a = (225 - b * 52) / 8
Calculate the values:
b = (10680 - 11700) / (3040 - 2704)
= -1020 / 336
= -3.036
a = (225 - (-3.036) * 52) / 8
= (225 + 157.872) / 8
= 382.872 / 8
= 47.859
Therefore, the least squares regression line of y on x is y = 47.859 - 3.036x.