Question

# Suppose you have a cross-country dataset with values for GDP (yi) and investment in research &...

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.

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.

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