Question
The table shows the fat and Calorie content for several snack foods. On a separate sheet of graph paper, construct a scatter plot. Then draw and assess a line that seems to represent the data.
Fat (g) 1 6 7 8 12 18 20
Calories 200 222 239 274 338 339 385
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)
The slope of the line is close to 10.
Disable choicecross out
B)
The slope of the line is close to 0.75.
Disable choicecross out
C)
Most of the points lie close to the line.
Disable choicecross out
D)
The line is not a good fit for the data.
Disable choicecross out
E)
The line passes through the origin
Disable choicecross out
F)
The calorie content of snack foods can be estimated by the grams of fat that they contain.
Fat (g) 1 6 7 8 12 18 20
Calories 200 222 239 274 338 339 385
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)
The slope of the line is close to 10.
Disable choicecross out
B)
The slope of the line is close to 0.75.
Disable choicecross out
C)
Most of the points lie close to the line.
Disable choicecross out
D)
The line is not a good fit for the data.
Disable choicecross out
E)
The line passes through the origin
Disable choicecross out
F)
The calorie content of snack foods can be estimated by the grams of fat that they contain.
Answers
GPT-4o mini
To analyze the data and select the true statements regarding the scatter plot and line of best fit for the given snack food data, let's first summarize the dataset:
**Fat (g)**: 1, 6, 7, 8, 12, 18, 20
**Calories**: 200, 222, 239, 274, 338, 339, 385
1. **Creating the scatter plot**: By plotting fat content on the x-axis and calorie content on the y-axis, you would typically see a positive linear relationship, suggesting that as fat content increases, calorie content generally increases.
2. **Drawing the line of best fit**: The line would ideally pass through the middle of the data points and should follow the general trend of the data.
Now let's assess each of the provided statements based on the characteristics of the scatter plot and the line of best fit:
A) **The slope of the line is close to 10.**
- This is likely false. Given the data values, the slope should reflect the change in calories for each additional gram of fat, suggesting a steeper slope, likely greater than 10.
B) **The slope of the line is close to 0.75.**
- This is also likely false for the same reasons as statement A; the slope calculated seems to be higher than that.
C) **Most of the points lie close to the line.**
- This can be true. If the line is a good fit and closely follows the trend established by the data points, then most points would be near the line.
D) **The line is not a good fit for the data.**
- This is likely false if the line has been drawn accurately according to the trend of the points.
E) **The line passes through the origin.**
- This is likely false as well; the line of best fit typically does not pass through (0, 0) unless the dataset indicates that both variables can be zero at the same time, which in this context (fat and calories) isn't likely.
F) **The calorie content of snack foods can be estimated by the grams of fat that they contain.**
- This can be true as the scatter plot suggests a relationship whereby calorie content can reasonably be predicted based on the grams of fat.
### Conclusion:
Based on the analysis above, the likely true statements are:
- **C) Most of the points lie close to the line.**
- **F) The calorie content of snack foods can be estimated by the grams of fat that they contain.**
You may want to confirm by referencing your actual scatter plot and line of best fit.
**Fat (g)**: 1, 6, 7, 8, 12, 18, 20
**Calories**: 200, 222, 239, 274, 338, 339, 385
1. **Creating the scatter plot**: By plotting fat content on the x-axis and calorie content on the y-axis, you would typically see a positive linear relationship, suggesting that as fat content increases, calorie content generally increases.
2. **Drawing the line of best fit**: The line would ideally pass through the middle of the data points and should follow the general trend of the data.
Now let's assess each of the provided statements based on the characteristics of the scatter plot and the line of best fit:
A) **The slope of the line is close to 10.**
- This is likely false. Given the data values, the slope should reflect the change in calories for each additional gram of fat, suggesting a steeper slope, likely greater than 10.
B) **The slope of the line is close to 0.75.**
- This is also likely false for the same reasons as statement A; the slope calculated seems to be higher than that.
C) **Most of the points lie close to the line.**
- This can be true. If the line is a good fit and closely follows the trend established by the data points, then most points would be near the line.
D) **The line is not a good fit for the data.**
- This is likely false if the line has been drawn accurately according to the trend of the points.
E) **The line passes through the origin.**
- This is likely false as well; the line of best fit typically does not pass through (0, 0) unless the dataset indicates that both variables can be zero at the same time, which in this context (fat and calories) isn't likely.
F) **The calorie content of snack foods can be estimated by the grams of fat that they contain.**
- This can be true as the scatter plot suggests a relationship whereby calorie content can reasonably be predicted based on the grams of fat.
### Conclusion:
Based on the analysis above, the likely true statements are:
- **C) Most of the points lie close to the line.**
- **F) The calorie content of snack foods can be estimated by the grams of fat that they contain.**
You may want to confirm by referencing your actual scatter plot and line of best fit.