Linear Regression - Problems with Solutions

Understanding Simple Linear Regression | Graphing & Examples

Problem 7 Consider fitting a simple linear regression model through the origin, Y = β1 X ϵ, to a set of data using the least squares method.(a) Give an example of situation where fitting the model Y = β1 X ϵ is justified by theoretical or other physic and material considerations.(b) Show that the least squares estimate of β1 is as given by β̂1̂ = (∑i=1^n yi xi)/(∑i=1^n xi^2).(c) Show that the residuals e1, e2, …, en will not necessarily add up to zero.