Question
The table shows the times of the gold, silver, and bronze medal winners for the men’s 100-meter race (in seconds) for 10 Olympic Games.
Find a linear model using the mean time data points from 1992 and 2004. Which is the BEST interpretation of the slope?
Responses
A The slope −0.05 means that for each calendar year, the predicted mean time increases by 0.05 seconds.The slope −0.05 means that for each calendar year, the predicted mean time increases by 0.05 seconds.
B The slope −0.0125 means that for each calendar year, the predicted mean time increases by 0.0125 seconds.The slope −0.0125 means that for each calendar year, the predicted mean time increases by 0.0125 seconds.
C The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.
D The slope −0.0125 means that for each calendar year, the predicted mean time decreases by 0.0125 seconds.
Find a linear model using the mean time data points from 1992 and 2004. Which is the BEST interpretation of the slope?
Responses
A The slope −0.05 means that for each calendar year, the predicted mean time increases by 0.05 seconds.The slope −0.05 means that for each calendar year, the predicted mean time increases by 0.05 seconds.
B The slope −0.0125 means that for each calendar year, the predicted mean time increases by 0.0125 seconds.The slope −0.0125 means that for each calendar year, the predicted mean time increases by 0.0125 seconds.
C The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.
D The slope −0.0125 means that for each calendar year, the predicted mean time decreases by 0.0125 seconds.
Answers
Answered by
GPT-4o mini
To find the best interpretation of the slope for a linear model using mean time data points from 1992 and 2004 for the men’s 100-meter race, we need to establish the context for the slope.
Let's understand that if we are calculating a linear regression model to predict the mean time based on the year, the slope represents the rate of change of the mean time with respect to each calendar year.
If we have a slope of –0.0125 (or –0.05), this indicates a negative trend, meaning that as the years progress (from 1992 to 2004), the mean time for the event is decreasing, not increasing.
From the options:
- A and B describe increases in time, which is not correct given a negative slope.
- C states that the time decreases by 0.05 seconds per calendar year, which is a valid interpretation if the slope is –0.05.
- D states that the time decreases by 0.0125 seconds per calendar year, which is valid if the slope is –0.0125.
Thus, to determine the best interpretation, we would need the exact values of the mean times from 1992 and 2004 to calculate the slope accurately. However, assuming we are discussing and if the calculated slope is indeed –0.0125, the correct interpretation would be:
**D. The slope −0.0125 means that for each calendar year, the predicted mean time decreases by 0.0125 seconds.**
If the calculated slope were –0.05, the correct interpretation would be:
**C. The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.**
### Conclusion:
The correct answer predominantly depends on the calculated slope value. If your slope was found to be –0.0125, then option D would be correct. If your slope was found to be –0.05, then option C would be correct.
Let's understand that if we are calculating a linear regression model to predict the mean time based on the year, the slope represents the rate of change of the mean time with respect to each calendar year.
If we have a slope of –0.0125 (or –0.05), this indicates a negative trend, meaning that as the years progress (from 1992 to 2004), the mean time for the event is decreasing, not increasing.
From the options:
- A and B describe increases in time, which is not correct given a negative slope.
- C states that the time decreases by 0.05 seconds per calendar year, which is a valid interpretation if the slope is –0.05.
- D states that the time decreases by 0.0125 seconds per calendar year, which is valid if the slope is –0.0125.
Thus, to determine the best interpretation, we would need the exact values of the mean times from 1992 and 2004 to calculate the slope accurately. However, assuming we are discussing and if the calculated slope is indeed –0.0125, the correct interpretation would be:
**D. The slope −0.0125 means that for each calendar year, the predicted mean time decreases by 0.0125 seconds.**
If the calculated slope were –0.05, the correct interpretation would be:
**C. The slope −0.05 means that for each calendar year, the predicted mean time decreases by 0.05 seconds.**
### Conclusion:
The correct answer predominantly depends on the calculated slope value. If your slope was found to be –0.0125, then option D would be correct. If your slope was found to be –0.05, then option C would be correct.