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STA2020F 2006 TEST 2 SOLUTIONS Q3-5

# STA2020F 2006 TEST 2 SOLUTIONS Q3-5 - Question 3 a H0 1 = 2...

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Question 3 a) H 0 : β 1 = β 2 = 0 H 1 : At least one of the β i s is not equal to zero p-value of F-test = 1.07E-26 ≈ 0 Conclusion: There is overwhelming evidence to infer that at least one of the explanatory variables is linearly related to per capita income. (3) b) For every percent increase in the percentage of the population under 15, per capita income decreases on average by \$30.045 holding continent constant. (2) c) b 2 = 273.4328. The average per capita income in Latin America countries is \$273.4328 higher than per capita income in African countries, keeping the percentage of the population under 15 constant (or for a given percentage of the population under 15). (2) d) Predicted value = 1415.5549 - 30.0455 x 40 + 273.4328 x 1 = 487.16645. The average per capita income is \$487.16645. (1) e) H 0 : β 2 = 0, H 1 : β 2 > 0 p-value = 1.48E-20/2 = 0.74E-20 (remember the test in the Excel output is two sided) Conclusion: There is overwhelming evidence to infer that per capita incomes are significantly higher in Latin American countries. (3) f)

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