Refer to Exercise 13.67. When unemployment rate of a country is added as an additional predictor to the model already containing CO2 and percentage of population not using the Internet, we get the following output.

a. Interpret the sign of the coefficient for unemployment. Is this the direction of the effect you would expect?
b. Is the coefficient for unemployment significantly different from zero? Explain. Does this automatically mean unemployment is unrelated to GDP? 

c. What measure would you use to investigate whether unemployment helps in predicting GDP?

d. R² increases from 94.26% to 94.28% when adding unemployment to the model with CO₂ and NoInternet. Explain what this means.

Exercise 13.67

Consider predicting the per capita GDP (gross domestic product, in thousands of dollars), of a country, using x₁ = carbon dioxide emissions per capita (in metric tons) and x₂ = percent of country population not using the Internet. Based on data for several countries, the following computer output was obtained:

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Coefficients: Std. Error Pr (>|t|) Estimate (Intercept) 38923 813 - 395 7259 5.4 0.0007 CO2 NoInternet 282 2.9 0.0204 58 -6.9 0.0001 606 Unemployed 107 0.2 0.8645 Coefficients: Estimate Pr(>|t|) Std. Error 39892 798 -399 Intercept 4474 8.9 0.0000 CO2 254 3.1 0.0119 NoInternet 51 -7.8 0.0000