A regression model examining the amount of distance a long distance runner runs (in miles) to predict the amount of fluid the runner drinks (ounces) has a slope of 4.6. Which interpretation is appropriate?
A) The correlation is needed to interpret this value.
B) A runner drinks a minimum of 4.6 oz.
C) We predict 4.6 miles for every ounce that is drunk.
D) We predict for every mile run, the runner drinks 4.6 more ounces.
E) Each mile adds 4.6 more ounces.
The correct answer and explanation is :
The correct answer is D) We predict for every mile run, the runner drinks 4.6 more ounces.
Explanation:
In a regression model, the slope (in this case, 4.6) represents the change in the dependent variable (fluid consumption, measured in ounces) for each unit change in the independent variable (distance run, measured in miles). The slope of 4.6 means that for each additional mile that the runner runs, the amount of fluid they drink increases by 4.6 ounces. This relationship suggests a positive correlation: as the distance run increases, so does the fluid consumption, and the rate of increase in fluid consumption is 4.6 ounces per mile run.
Let’s go through the other options to explain why they are incorrect:
- A) The correlation is needed to interpret this value.
This is not true because the correlation coefficient is not required to interpret the slope. The slope itself provides direct information about the relationship between the independent and dependent variables. The correlation tells us about the strength and direction of the linear relationship but is not necessary to understand the slope’s meaning. - B) A runner drinks a minimum of 4.6 oz.
This is incorrect because the slope tells us the change in fluid consumption per mile run, not the minimum amount of fluid drunk. The slope does not directly describe the starting or minimum amount of fluid consumed. - C) We predict 4.6 miles for every ounce that is drunk.
This is a misinterpretation of the slope. The slope indicates how the dependent variable (fluid consumption) changes with respect to the independent variable (miles run), not the reverse. - E) Each mile adds 4.6 more ounces.
While this might seem close to the correct answer, the wording is slightly off. The correct interpretation is that for every additional mile run, the runner drinks 4.6 more ounces of fluid, rather than saying “each mile adds,” which can be seen as an unclear description of the change.
Thus, D is the best interpretation because it directly explains that the increase in fluid consumption is associated with each additional mile the runner runs.