Well-being has become in important development indicator beyond economic welfare. There are several components of wellbeing and different measures to quantify it. A development economist collects subjective wellbeing (SWB) data at the level of individuals across 50 countries by asking respondents to rate their wellbeing on a scale from 0-10 (where 10 is the best state) and stores it in the file Countries . Develop a model to predict the mean SWB of a country based on per capita GDP (measured in purchasing power parity, current international thousand dollars) and annual population growth level (\%)).

a. State the multiple regression equation.

b. Interpret the meaning of the slopes in this equation.

c. Predict the mean SWB of a country that has a per capita GDP of \(\$ 40,000\) and \(0.5 \%\) population growth.

d. Perform a residual analysis on your model and determine whether the regression assumptions are valid.

e. Is there a significant relationship between SWB of a country and the two independent variables (per capita GDP and population growth) at the 0.05 level of significance?

f. Determine the \(p\)-value in (e) and interpret its meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted \(r^{2}\).

i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

j. Determine the \(p\)-values in (i) and interpret their meaning.

k. Construct a 95\% confidence interval estimate of the population slope between SWB and population growth.

1. Compute and interpret the coefficients of partial determination.

m. Which is more important in predicting SWB? Explain.