Question

Consider the bivariate regression results below for a model of infant mortality rate (deaths per 1000 live births) as a function of GDP per capita measured in $1,000s. The regression model was estimated with data for a sample of 42 countries.

Parameter Estimate Standard Error

Constant 87.53 6.18

GDP per capita -2.21 0.32

a) How much does the regression model predict the infant mortality rate will change from a 12 unit

increase in GDP per capita (i.e., $10,000 per capita increase)? [7 points]

b) According to the regression, what does a country’s GDP per capita have to be for the infant mortality

rate to be below 6.0 on average (which is the rate in most Western European countries)? [7 points]

c) Test the null hypothesis that every $1,000 increase in GDP per capita reduces the expected infant

mortality rate by less than 2 deaths per 1000 live births. Can you reject this null hypothesis at the 1% significance level? [8 points]

Answer 1

(a) Here the regression equation is

Infant Mortality Rate (I) = 87.53 - 2.21 * GDP per capita

from a 12 unit increase in GDP per capita (i.e., $10,000 per capita increase), there will be decrease of 2.21 * 12 = 26.52  deaths per 1000 live births.

(b) According to the regression, a country’s GDP per capita have to be for the infant mortality rate to be below 6.0 on average is lets say x.

then,

6 = 87.53 - 2.21 * GDP per capita

GDP per capita = (87.53 - 6)/2.21 = 36.89 (in $ 10,000)

(c) H0  : =2 deaths per 1000 live births

Ha : < 2 deaths per 1000 live births

t = (-2.21+2)/0.32 = -0.66

so here t(critical) = TINV(0.02, 40) = 2.423

so here l t l < t(critical) so we would fail to reject the null hypothesis and can conlcude that for every $1,000 increase in GDP per capita reduces the expected infant mortality rate by not less than 2 deaths per 1000 live births.