Researchers developed a model to explain the age gap between husbands and wives at first marriage. The model is below:

y̅ = 0.0321x1 + 0.9848x2 + 0.5391x3 - 0.000145x42 + 3.8483

where

y: Age gap at first marriage (male - female)

x1: Percent of children aged 10 to 14 involved in child labor

x2: Indicator variable where 1 is an African country, 0 otherwise

x3: Percent of the population that is Muslim

x4: Percent of the population that is literate

(a) Use the model to predict the age gap at first marriage for an African country where the percent of children aged 10 to 14 who are involved in child labor is 12, the percent of the population that is Muslim is 30, and the percent of the population that is literate is 75.

(b) What would be the mean difference in age gap between an African country and a non-African country?

(c) Interpret the coefficient of "percent of children aged 10 to 14 involved in child labor."

(d) The coefficient of determination for this model is 0.593. Interpret this result.

(e) The P-value for the test H1: β1 ≠ 0 versus H1: β1 ≠ 0 is 0.008. What would you conclude about this test?