A social economist studies the relationship between a happiness index Y, life ex

Question

A social economist studies the relationship between a happiness index Y, life expectancy X_1, and a freedom index X_2 for individual countries. She examines two different models, the first had one predictor and the second has two predictors (this problem). Write the estimated MR equation for Model 2. Interpret b_2 in the context of the problem. Conduct a NATDRC model utility test at a 0.05 level of significance. Interpret the multiple coefficient of determination. Estimate the happiness index for a country where the life expectancy is 75 years and the freedom index is 4.0.

Explanation / Answer

a. Estimated MR equation for model 2 is, y = 1.31+0.05*x1+0.34*x2.

b. b2 = Coef(x2) = 0.34, it means that Happiness index increases by 0.34 with an increase of 1 unit of freedom Index.

d. Multiple coef of determination, multiple R-squared = 0.630 implies that 63% of the variation in Happiness Index can be explained by variations of life expectancy and freedom index.

e. Here applying to the formula (a), Happiness Index = 1.31+0.05*75+0.34*4 = 6.42

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