Question

an agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of bushels of corn produced. this is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of nitrogen.
y = 0.43x + 28.5
what is the meaning of the slope of the regression line?
a. for every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
b. for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
c. for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
d. for every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.

Explanation:

The regression line is in the form \( y = mx + b \), where \( m \) is the slope. Here, \( m = 0.43 \), \( x \) is pounds of nitrogen, and \( y \) is bushels of corn. The slope represents the change in \( y \) per unit change in \( x \). So for each 1 - pound increase in nitrogen (\( x \)), corn yield (\( y \)) increases by 0.43 bushels. Option B matches this interpretation.

Answer:

B. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.