Given that; Sigma*x = 52; n = 8; 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 calculate the least squares regression line of y on x in the form of y = a + bx, we need to find the values of a and b.
Step 1: Calculate the mean of x (x̄) and the mean of y (ȳ).
x̄ = Sigma*x / n = 52 / 8 = 6.5
ȳ = y / n = 225 / 8 = 28.125
Step 2: Calculate the sum of squares of x (SSx) and the sum of squares of y (SSy).
SSx = Sigma * x^2 - n * (x̄)^2 = 380 - 8 * (6.5)^2 = 380 - 338 = 42
SSy = Sigma * y^2 - n * (ȳ)^2 = 7007 - 8 * (28.125)^2 = 7007 - 6314.06 = 692.94
Step 3: Calculate the sum of cross-products (Sxy).
Sxy = Sigma * xy - n * x̄ * ȳ = 1335 - 8 * 6.5 * 28.125 = 1335 - 14625 = -13290
Step 4: Calculate the slope (b):
b = Sxy / SSx = -13290 / 42 = -316.43
Step 5: Calculate the intercept (a):
a = ȳ - b * x̄ = 28.125 - (-316.43) * 6.5 = 28.125 + 2055.295 = 2083.42
Therefore, the least squares regression line of y on x is y = 2083.42 - 316.43x.