Suppose we are given the set of data points
(x1, y1), (x2, y2),..., (xn, yn)
and that we are interested in finding a straigt line that "best" fits that data. We will begin with the linear model
Yi = α-β(xi - x̄) + εi
where we assume that for a partiular value of x, that the value of Y will differ from its mean by some random ammount ε and that the
distribution of ε is N(0,σ). It can be show that the estimate for α is
α̂ =ȳ
and that the estimate for β is
̂β =
∑iyi(xi - x̄)2/ ∑i(xi - x̄)2
To use the linear regression calculator below, input your sample data as a comma separated list and hit go! You will see you two plots. The first will show your data along with the
computed regression line,
ŷ = E[Y] = α̂-̂β(x - x̄)
and the second will plot all of the residuals:
yi - ŷi .
x:
y:
