The formula for linear least-squares method is
y-bar y=sigma_(xy)/(sigma_x^2)(x-bar x), where
bar x, bar y: average of x and y, respectively.
sigma_x^2: variance of x
sigma_(xy): covarience of x and y
First, calculate bar x and bar y.
bar x=(-2+8+10+15)/4=7.75
bar y=(50+75+103+146)/4=93.5
Then, calculate sigma_x^2 and sigma_(xy).
sigma_x^2=((-2-7.75)^2+(8-7.75)^2+(10-7.75)^2+(15-7.75)^2)/4
=38.1875
sigma_(xy)=((-2-7.75)・(50-93.5)+(8-7.75)・(75-93.5)+(10-7.75)・(103-93.5)+(15-7.75)・(146-93.5))/4
=205.375 (sorry for the ugly format!)
Therefore, the formula of the line is
y-93.5=38.1875/205.375(x-7.75)
y-93.5=5.3781(x-7.75)
y-93.5=5.3781x-41.680
y=5.38x+51.82
![enter image source here]()
If you can use Microsoft Excel, you can calculate the average,variance and covariance with AVERAGE, VARP and COVAR function, respectively.
