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.
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.
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 scatter plot and line drawn from the provided data, let's analyze them one by one:
### **Statements:**
**A) Most of the points lie close to the line.**
- **Assessment:** If the scatter plot indicates that many points are close to the fitted line, this statement would be true. However, without seeing the actual plot, we cannot definitively confirm this.
**B) The line is not a good fit for the data.**
- **Assessment:** This would depend on how well the line approximates the data points. If the points are widely spread and far from the line, this statement may be true.
**C) The slope of the line is close to 1.25.**
- **Assessment:** To determine whether the slope is close to 1.25, one would need to calculate the slope based on the plotted line. Given the MPG and GRG relationship, this is unlikely to be true, as the slope typically represents the change in GRG with each unit change in MPG.
**D) The slope of the line is close to 0.25.**
- **Assessment:** Similar to C, this would depend on the actual slope of the fitted line. If the relationship between MPG and GRG is relatively shallow, this could be true.
**E) The line passes through the origin.**
- **Assessment:** This would need to be checked against the fitted line. Most linear relationships of this kind do not pass through the origin unless data indicates that an MPG of 0 corresponds to a GRG of 0.
**F) A car's greenhouse gas rating can be estimated by its average MPG.**
- **Assessment:** If there is a clear trend in the scatter plot showing that higher MPG corresponds to lower GRG (which is likely), this statement would be true.
### **Conclusion:**
To determine which statements are true, you should visually assess the scatter plot. Based on typical relationships between MPG and greenhouse gas ratings, we can hypothesize:
- Statements A and F are likely true if the data shows a strong correlation.
- Statements B and C seem less likely to be true based on common trends.
- D would need specific calculations of the slope.
- E is usually false for this type of data.
In conclusion, it is important to create the scatter plot to accurately assess the situation.
### **Statements:**
**A) Most of the points lie close to the line.**
- **Assessment:** If the scatter plot indicates that many points are close to the fitted line, this statement would be true. However, without seeing the actual plot, we cannot definitively confirm this.
**B) The line is not a good fit for the data.**
- **Assessment:** This would depend on how well the line approximates the data points. If the points are widely spread and far from the line, this statement may be true.
**C) The slope of the line is close to 1.25.**
- **Assessment:** To determine whether the slope is close to 1.25, one would need to calculate the slope based on the plotted line. Given the MPG and GRG relationship, this is unlikely to be true, as the slope typically represents the change in GRG with each unit change in MPG.
**D) The slope of the line is close to 0.25.**
- **Assessment:** Similar to C, this would depend on the actual slope of the fitted line. If the relationship between MPG and GRG is relatively shallow, this could be true.
**E) The line passes through the origin.**
- **Assessment:** This would need to be checked against the fitted line. Most linear relationships of this kind do not pass through the origin unless data indicates that an MPG of 0 corresponds to a GRG of 0.
**F) A car's greenhouse gas rating can be estimated by its average MPG.**
- **Assessment:** If there is a clear trend in the scatter plot showing that higher MPG corresponds to lower GRG (which is likely), this statement would be true.
### **Conclusion:**
To determine which statements are true, you should visually assess the scatter plot. Based on typical relationships between MPG and greenhouse gas ratings, we can hypothesize:
- Statements A and F are likely true if the data shows a strong correlation.
- Statements B and C seem less likely to be true based on common trends.
- D would need specific calculations of the slope.
- E is usually false for this type of data.
In conclusion, it is important to create the scatter plot to accurately assess the situation.