A veterinarian collected data on the association between age and mass of Boxer puppies. A line of best fit was computed. The
equation for the line is y = 17.5 + 480.
Age and Mass of Boxer Puppies
Which BEST interprets the slope of the linear model?
A. The predicted mass of a Boxer puppy at birth.
B. Each additional day is associated with an additional 17.5 grams of mass.
C. Each additional day is associated with an additional 480 grams of mass.
D. Every 17.5 days is associated with an additional 480 grams of mass.
The equation for the line of best fit you've provided seems to be incomplete as it stands, as the usual form for a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope (m) represents the change in the dependent variable (y; in this case, mass) for each unit change in the independent variable (x; in this case, age), while the y-intercept (b) represents the value of the dependent variable when the independent variable is zero.
However, if we interpret your equation y = 17.5 + 480 as having an implied independent variable (age), it could be rewritten as y = 17.5x + 480, which would make more sense. In this case, the slope would be 17.5, and the y-intercept would be 480.
Assuming the correct equation should indeed be y = 17.5x + 480, the slope of the linear model (17.5) represents how much the mass of a Boxer puppy changes for each unit increase in age.
Here are the choices with this interpretation:
A. The predicted mass of a Boxer puppy at birth.
- This is incorrect because the y-intercept (480 in this case) would represent the mass at birth, not the slope.
B. Each additional day is associated with an additional 17.5 grams of mass.
- This is the correct interpretation. The slope indicates the increase in mass (grams) for each additional day of age.
C. Each additional day is associated with an additional 480 grams of mass.
- This is incorrect because 480 is the y-intercept, not the slope.
D. Every 17.5 days is associated with an additional 480 grams of mass.
- This is incorrect. While it mixes both numbers, it incorrectly associates the y-intercept with the unit change in days suggested by the slope.
The best interpretation is B: Each additional day is associated with an additional 17.5 grams of mass.