Question

Suppose I estimate a regression where the dependent variable is the life expectancy (in years) in a country and the regressor is the percentage of a country's GDP that comes from the agricultural sector. Our results give us a prediction equation of Y = 78 - 0.5*X. What is the most accurate interpretation of the slope coefficient in these results?

A-If the life expectancy in a country increases by 1 year, the share of GDP coming from agriculture drops by 0.5 percent
B-If the life expectancy in a country increases by 1 year, the share of GDP coming from agriculture drops by 0.5 percentage points
C-If the share of GDP coming from agriculture increases by 1 percent, life expectancy drops by 0.5 years.
D-If the share of GDP coming from agriculture increases by 1 percentage point, life expectancy drops by 0.5 years

Answer 1

The slope -0.5 in the equation Y = 78 - 0.5*X indicates that for every increase of 1 percentage point in the GDP from agriculture, the life expectancy decreases by 0.5 years.

Step-by-step explanation:

The correct interpretation of the slope coefficient in the provided regression equation “Y = 78 - 0.5*X”, where ‘Y’ represents life expectancy in years and ‘X’ represents the percentage of a country's GDP from agriculture, is D: “If the share of GDP coming from agriculture increases by 1 percentage point, life expectancy drops by 0.5 years.” This is because in the slope-intercept form of a linear equation, the slope, which is the coefficient attached to the independent variable ‘X’, conveys how the dependent variable ‘Y’ is expected to change with a one-unit increase in ‘X’.