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 and x is measured in pounds of nitrogen. y = 0.43x + 28.7 what is the meaning of the y-intercept of the regression line? a. when no nitrogen is added to the field, 28.7 bushels of corn are produced. b. when 28.7 pounds of nitrogen is added to the field, no bushels of corn are produced. c. when 0.43 pounds of nitrogen is added to the field, 28.7 bushels of corn are produced. d. when 28.7 pounds of nitrogen is added to the field, 0.43 bushels of corn are produced.

Explanation:

The regression line is \( y = 0.43x + 28.7 \), where \( x \) is pounds of nitrogen and \( y \) is bushels of corn. The y - intercept occurs when \( x = 0 \) (no nitrogen added). Substituting \( x = 0 \) into the equation, we get \( y=0.43(0)+28.7 = 28.7 \). This means when no nitrogen (\( x = 0 \)) is added, the corn production (\( y \)) is 28.7 bushels. Option A matches this interpretation. Option B misinterprets the y - intercept (it would be when \( y = 0 \), not \( x = 28.7 \)). Option C uses \( x = 0.43 \) which is incorrect. Option D misinterprets both \( x \) and \( y \) values.

Answer:

A. When no nitrogen is added to the field, 28.7 bushels of corn are produced.