Consider the Classical Linear Regression Model (CLRM) Y = α +βX +ε where X denotes the independent GNI per capita, Atlas method (current US$), Y is the dependent variable Life expectancy at birth, total (years), α and β are unknown constants and ε is a random variable. Use a calculator and your sample to calculate ∑X, ∑Y, ∑XY and ∑X2. Use these values to write down the pair of ‘normal equations’ the solutions of which give the constant term (a) and the slope coefficient (b) of the fitted Ordinary Least Squares line Y = a + bX. i.
Write down the equivalent matrix representation of the normal equations you have written in part.
Explain how matrix algebra can be used to solve for the terms a and b.
Data will be provided on request and further instructions in order to make the analysis smooth.