Question

1. To establish the impact of population of GDP, you collect quarterly data on the two variables from the period 1980 to 2016 and obtain the following values;

i=1nyi2=54163.6 ;       i=1nxi2=59.225 ; i=1nxiyi=-1491.885 ;            

i=1nYi=6278; i=1nXi=199.5;    i=1nYi2=3995492;    i=1nXi2=4039.25;

i=1nXiYi=111756

Using these values, you estimate the model;

GDPi=β0+β1Populationi+Ui

1. Based on the above model, derive the parameters using OLS.          [6 Marks]
2. Using the data above, compute the estimates β0 and β1 and provide and economic interpretation.                                                                      [6 Marks       

Answer 1

In statistics, ordinary least squares (OLS) is a type of linear least squares method for estimating the unknown parameters in a linear regression model.

Ordinary Least Squares (OLS) is a method of point estimation of parameters that minimizes the function defined by the sum of squares of these residuals (or distances) with respect to the parameters. ... Recall that parameter estimation is concerned with finding the value of a population parameter from sample statistics.

In econometrics, Ordinary Least Squares (OLS) method is widely used to estimate the parameter of a linear regression model. OLS estimators minimize the sum of the squared errors (a difference between observed values and predicted values).

rdinary Least Squares or OLS is one of the simplest (if you can call it so) methods of linear regression. The goal of OLS is to closely "fit" a function with the data. It does so by minimizing the sum of squared errors from the data.

OLS: Ordinary Least Square Method

1. Set a difference between dependent variable and its estimation:
2. Square the difference:
3. Take summation for all data.
4. To get the parameters that make the sum of square difference become minimum, take partial derivative for each parameter and equate it with zerothe properties of OLS estimators were discussed because it is the most widely used estimation technique. OLS estimators are BLUE (i.e. they are linear, unbiased and have the least variance among the class of all linear and unbiased estimators).