Question
The table shows the average combined miles per gallon (MPG) and greenhouse gas (GRG) rating for certain mid-size cars. On a separate sheet of graph paper, construct a scatter plot. Then draw and assess a line that seems to represent the data.
Average MPG 22 25 31 28 16 26 35 41 24 32 30 23
GRG Rating 5 6 7 7 3 6 8 9 5 8 7 5
Which of the following statements are true for the scatter plot and line that you drew? Select all that apply.
Multiple select question.
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A)
Most of the points lie close to the line.
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B)
The line is not a good fit for the data.
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C)
The slope of the line is close to 1.25
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D)
The slope of the line is close to 0.25.
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E)
The line passes through the origin.
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F)
A car's greenhouse gas rating can be estimated by its average MPG
Average MPG 22 25 31 28 16 26 35 41 24 32 30 23
GRG Rating 5 6 7 7 3 6 8 9 5 8 7 5
Which of the following statements are true for the scatter plot and line that you drew? Select all that apply.
Multiple select question.
Disable choicecross out
A)
Most of the points lie close to the line.
Disable choicecross out
B)
The line is not a good fit for the data.
Disable choicecross out
C)
The slope of the line is close to 1.25
Disable choicecross out
D)
The slope of the line is close to 0.25.
Disable choicecross out
E)
The line passes through the origin.
Disable choicecross out
F)
A car's greenhouse gas rating can be estimated by its average MPG
Answers
GPT-4o mini
To evaluate the statements based on the given data for average MPG and GRG rating, we first need to understand the relationship between the two variables and assess the line we would draw on the scatter plot of this data.
1. **Most of the points lie close to the line.**
- This statement could be true or false depending on how well the points cluster around the line we draw. Generally, if the points exhibit a linear trend, this could be assessed as true.
2. **The line is not a good fit for the data.**
- If the scatter plot shows a clear linear trend, then this statement would be false. Conversely, if points are widely scattered with no discernible linear relationship, this could be true.
3. **The slope of the line is close to 1.25.**
- To evaluate this, we would need to calculate the slope based on the scatter plot. Typically, with average MPG ranging from 16 to 41 and GRG ratings from 3 to 9, a slope of 1.25 might be plausible, but without exact calculations, we can't definitively say if it's true.
4. **The slope of the line is close to 0.25.**
- Similar to the previous point, without exact slope calculations, we cannot determine if this is true. It is, however, less likely given the MPG data, which suggests a steeper increase.
5. **The line passes through the origin.**
- For the line to pass through the origin, both variables (MPG and GRG) would need to be zero at the same point, which is not true in this dataset.
6. **A car's greenhouse gas rating can be estimated by its average MPG.**
- Given the context of the problem, the relationship described suggests that there is an inverse correlation where higher MPG typically leads to lower greenhouse gas ratings. If a relationship is observed in the scatter plot, this statement can be true.
### Conclusion:
Based on general trends and assumptions:
- A) could be true if the points cluster well around the line.
- B) could be false if the data shows a good linear trend.
- C) is indeterminate without calculations.
- D) is also indeterminate without calculations but seems unlikely to be accurate.
- E) is false as the data likely does not start at 0 for both variables.
- F) may be true if the relationship between MPG and GRG is consistent and linear.
To accurately assess the validity of each statement, plotting the scatter plot and calculating the line of best fit is necessary.
1. **Most of the points lie close to the line.**
- This statement could be true or false depending on how well the points cluster around the line we draw. Generally, if the points exhibit a linear trend, this could be assessed as true.
2. **The line is not a good fit for the data.**
- If the scatter plot shows a clear linear trend, then this statement would be false. Conversely, if points are widely scattered with no discernible linear relationship, this could be true.
3. **The slope of the line is close to 1.25.**
- To evaluate this, we would need to calculate the slope based on the scatter plot. Typically, with average MPG ranging from 16 to 41 and GRG ratings from 3 to 9, a slope of 1.25 might be plausible, but without exact calculations, we can't definitively say if it's true.
4. **The slope of the line is close to 0.25.**
- Similar to the previous point, without exact slope calculations, we cannot determine if this is true. It is, however, less likely given the MPG data, which suggests a steeper increase.
5. **The line passes through the origin.**
- For the line to pass through the origin, both variables (MPG and GRG) would need to be zero at the same point, which is not true in this dataset.
6. **A car's greenhouse gas rating can be estimated by its average MPG.**
- Given the context of the problem, the relationship described suggests that there is an inverse correlation where higher MPG typically leads to lower greenhouse gas ratings. If a relationship is observed in the scatter plot, this statement can be true.
### Conclusion:
Based on general trends and assumptions:
- A) could be true if the points cluster well around the line.
- B) could be false if the data shows a good linear trend.
- C) is indeterminate without calculations.
- D) is also indeterminate without calculations but seems unlikely to be accurate.
- E) is false as the data likely does not start at 0 for both variables.
- F) may be true if the relationship between MPG and GRG is consistent and linear.
To accurately assess the validity of each statement, plotting the scatter plot and calculating the line of best fit is necessary.