Question

Researchers studied the infant mortality rates in 1970 in n = 101 countries across four regions using multiple linear regression. The response is an infant mortality rate index. Two predictors were considered by the researchers: • Income index: a numeric predictor of the average income of each country. • Region: a categorical predictor of the region of the country with 4 categories: Africa (baseline), Americas (North and South America), Asia (Asia and Oceania), and Europe.

The R output of the multiple linear regression is given below.

Call:

lm(formula = infant ~ income + region)

Residuals: Min 1Q Median 3Q Max -1.5108 -0.3491 -0.0458 0.2804 2.9928 3

Coefficients:

Intercept: 6.40301

Income slope: -0.29939

Regions Americas slope: -.060233

RegionAsia slope: -0.72334

RegionEurope: -1.20282

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

(a) What is the slope term associated with the predictor income? Write a thorough interpretation of this slope term.

(b) The income index for the United States is 8.62. What is the predicted infant mortality rate index for the United States based on the regression line?

(c) The income index for Egypt, which is an African country, is 5.35. What is the predicted infant mortality rate index for Egypt based on the regression line?

Answer 1

The estimated regression equation to predict infant mortality rates is

where Income: is income index: a numeric predictor of the average income of each country

Region:Americas=1 if the country is from North and South Americas, else 0

Region:Asia=1 if the country is from Asia and Oceania, else 0

Region:Europe=1 if the country is from Europe, else 0

this means that if Region:Americas=Region:Asia=Region:Europe=0 then the country is from Africa (and hence this is the baseline)

a) The slope term associated with the predictor income is -0.29939.

The negative value of the slope indicates that the income index and infant mortality rate index are negatively correlated. That is they move in opposite direction. The negative value says that as the income index of a country increases (or as the  average income of a country increases), the  infant mortality rate index is predicted to drop, while we keep the region the same.

Further, we can say that if the income index of a country increases by 1 point, the predicted infant mortality rate index would reduce by 0.29939 for that country, while we keep the region the same.

b) The income index for the United States is 8.62. That means Income=8.62

The value of the variables Region:Americas=1, and Region:Asia=Region:Europe=0 for the United States

Using these values we get

ans: The predicted infant mortality rate index for the United States based on the regression line is 3.76

c) The income index for Egypt, which is an African country, is 5.35.

That means Income=5.35

The value of the variables Region:Americas=Region:Asia=Region:Europe=0 for Egypt which is in the baseline region Africa.

Using these values we get

ans:  The predicted infant mortality rate index for Egypt based on the regression line is 4.80