Classical Linear Regression Model

Project description

Task 1 is based on the dataset to be prepared as follows:
A. Go to http://data.worldbank.org/ .
Click on the option By Country on the top left-hand side of the page. Select a country from the list. For this country, collect the data on (i) Life expectancy at birth, total (years), (ii) GNI per

capita, Atlas method (current US$) and (iii) Improved water source, rural (% of rural population with access)
B. Acquire the data for a total of n randomly selected countries where n is an integer of your choice satisfying 15 ≤ n ≤ 30

C. Questions:
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 (i) above. (15 marks)
ii. Explain how matrix algebra can be used to solve for the terms a and b. (15 marks)
[Note: You are not required to give the solutions; simply explain the method.]

Task 2 (70 marks)
Consider the Classical Linear Regression Model (CLRM) Y = β1 + β2X2 +β3X3 + β4X4 + ɛ, where
Y ≡ IN ≡ Internet users; X2 ≡ Urban population; X3≡ Literacy Rate and X4 ≡ GDP.
Stata performed an OLS estimation of the model and produced the regression output below: