To interpret the slope of a linear regression model, we consider how the dependent variable (in this case, daily protein intake \( y \)) changes with respect to a one-unit change in the independent variable (bodybuilder's weight \( x \)).
If the slope is given as 1.5, it typically means that for each additional unit of the independent variable, the dependent variable increases by that amount. Here, we assume that the slope represents the relationship as follows:
- An additional 1 pound of bodyweight (independent variable) is associated with an increase of 1.5 grams of protein intake (dependent variable).
Looking at the options given:
- Option A ("An additional 1.5 grams of bodyweight is associated with an additional pound of protein intake.") does not accurately describe the relationship.
- Option B ("An additional 1.5 grams of protein intake is associated with an additional pound of bodyweight.") is also incorrect.
- Option C ("An additional 1.5 pounds of bodyweight is associated with an additional gram of protein intake.") does not represent the relationship correctly.
- Option D ("An additional 1.5 pounds of protein is associated with an additional gram of bodyweight.") is misleading.
Thus, none of the options correctly interprets the slope if we assume the slope indicates the increase in protein intake for each pound of bodyweight. Based on the slope as typically described, the correct interpretation would be: for every additional pound of bodyweight, there is an increase of 1.5 grams of protein intake. However, since this isn't listed, if you had to choose one response, you would consider the closest interpretation, but none directly fits the correct interpretation of the relationship.
Please check the exact context or provided numbers for the linear regression model, as there may be an error or misunderstanding in the options presented versus the model's slope.
3 answers