A study by the U.S. Small Business Administration modelled the GDP per capita of 24 of the countries in the Organisation for Economic Co-operation and Development (OECD). One analysis estimated the effect on GDP of economic regulations using an index of the degree of OECD economic regulation and other variables. The analyst found the following regression model:

Dependent variable is: GDP/Capita

R-squared = 97.4% R-squared (adjusted) = 96.6%

s = 2084 with 24 − 6 = 18 degrees of freedom

a) If we remove Primary Education from the model, the R² decreases to 97.3%, but the adjusted R² increases to 96.7%. How can that happen? What does it mean? Would you include Primary Education in this model?

Here’s a part of that regression:

Dependent variable is: GDP/Capita

R-squared = 97.3% R-squared (adjusted) = 96.7%

s = 2054 with 24$ – $5 = 19 degrees of freedom

b) Consider the t-statistic for OECD Regulation in the reduced model. That was the predictor of interest to this author. Do you agree with his conclusion that OECD regulation reduced GDP/Capita in these countries? Why do you think he chose to include Primary Education as a predictor? Explain.

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Sum of Squares Mean Square Source df F-ratio 2895078376 Regression 5 579015675 133 Residual 78158955 18 4342164 Variable Coeff SE(Coeff) t-ratio P-Value Intercept 10487.3 9431 1.11 0.2808 OECD Reg Index -1343.28 626.4 -2.14 0.0459 Ethnolinguistic Diversity -69.9875 -3.01 0.0075 23.26 14.00 0.0050 Int'l Trade/GDP 44.7096 3.19 Primary Education(%) -58.4084 86.11 -0.678 0.5062 1988 GDP/Capita 1.07767 <0.0001 0.0448 24.1 Variable Coeff SE(Coeff) t-ratio P-Value 4243.21 2022 |-1244.20 600.4 Ethnolinguistic Diversity -64.4200 21.45 Intercept OECD 2.10 0.0495 Reg Index -2.07 0.0521 -3.00 0.0073 Int'l Trade/GDP 40.3905 12.29 3.29 0.0039 1988 GDP/Capita 1.08492 0.0429 25.3 <0.0001