Question

Noah testes several men of different ages to see how many push ups they could complete in a row without resting. An approximate least squares regression line was used to predict the number of push ups from a given age of man

Answer 1

Estimator 'b' from sample regression function 'y = b0 + b1x + u' satisfies OLS, if Σu^2 = Σ (Y - y)^2 is minimum

Explanation:

Regression shows the relationship between independent (causal) & dependent (effected) variables.

As per given case : Independent variable = men's are = x ; dependent variable = number of push ups = y

• Population regression function [ PRF ] : Y | Xi = B0 + B1Xi
• Sample (estimated) regression function [SRF] : y = b0 + b1x + u

OLS [Ordinary Least Square] model is a method used for finding linear regression parametes (b's), such that it minimises the sum of squared residuals. Residuals are the error terms between PRF actual value & SRF estimated value

So, b's from SRF are OLS estimators if, Σu^2 = Σ (Y - y)^2 is minimum