Question

Suppose you have a cross-country dataset with values for GDP (yi) and investment in research & development (xi). Describe the method of ordinary least squares (OLS) to estimate the following univariate linear regression model, i.e.

yi = β0 + β1 xi + εi

In particular, describe in your words which are the dependent and the explanatory variables; how the OLS estimation method works; how to interpret the estimates for the coefficients β0 and β1; what is the coefficient of determination and what it is used for.

Answer 1

Here dependent variable is yi that is GDP and explanatory variable is xi that is investment in research and developement.

Method of OLS: first, set up the minimization problem that is the starting point for deriving the formulas for the OLS intercept and slope coefficient. That problem was, min βˆ0,βˆ1 X N i=1 (yi − βˆ 0 − βˆ 1xi)^2

Now derivate the above equation with respect to and then put it equal to 0 and solve both the equations simultanously. This is how get our OLS estimators, in short OLS estimator we can find by mininizing the square of errors.

Interpretation of   = an unit increase in xi will lead to   unit increase in yi.