Question
The scatter plot shows the relationship between combined SAT score and first semester college GPA. Which statements are correct? (hint: there is more than 1)
The image is a scatter plot showing a positive correlation between combined SAT scores and first-semester college GPA.
The image displays a scatter plot graph illustrating the relationship between combined SAT scores and first-semester college GPA. The horizontal x-axis represents the combined SAT score, ranging from approximately 1100 to 2300, marked with increments of 200. The vertical y-axis represents the first-semester college GPA, ranging from 2.0 to 4.0, marked with increments of 0.2. Individual data points, represented by blue dots, are scattered across the graph, showing the GPA achieved by students with various SAT scores. A black line of best fit is drawn through the data points, demonstrating a clear upward trend. This indicates a positive correlation, suggesting that higher SAT scores tend to be associated with higher first-semester GPAs. The overall mood and atmosphere of the image is objective and analytical, typical of a data representation within an academic or statistical context. There is no emotional content or artistic expression present; the image purely conveys quantitative information.
Responses
The line of best fit can be used to make predictions of GPA based on SAT score.
The line of best fit can be used to make predictions of GPA based on SAT score.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.
The line of best fit shows that the SAT score and GPA have a negative association.
The line of best fit shows that the SAT score and GPA have a negative association.
The line of best fit gives the best approximation of the association between SAT score and GPA.
The image is a scatter plot showing a positive correlation between combined SAT scores and first-semester college GPA.
The image displays a scatter plot graph illustrating the relationship between combined SAT scores and first-semester college GPA. The horizontal x-axis represents the combined SAT score, ranging from approximately 1100 to 2300, marked with increments of 200. The vertical y-axis represents the first-semester college GPA, ranging from 2.0 to 4.0, marked with increments of 0.2. Individual data points, represented by blue dots, are scattered across the graph, showing the GPA achieved by students with various SAT scores. A black line of best fit is drawn through the data points, demonstrating a clear upward trend. This indicates a positive correlation, suggesting that higher SAT scores tend to be associated with higher first-semester GPAs. The overall mood and atmosphere of the image is objective and analytical, typical of a data representation within an academic or statistical context. There is no emotional content or artistic expression present; the image purely conveys quantitative information.
Responses
The line of best fit can be used to make predictions of GPA based on SAT score.
The line of best fit can be used to make predictions of GPA based on SAT score.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.
The line of best fit shows that the SAT score and GPA have a negative association.
The line of best fit shows that the SAT score and GPA have a negative association.
The line of best fit gives the best approximation of the association between SAT score and GPA.
Answers
GPT-4o mini
Based on the description of the scatter plot and the properties of correlation and regression analysis, the following statements can be evaluated as correct or incorrect:
1. **The line of best fit can be used to make predictions of GPA based on SAT score.**
- **Correct.** A line of best fit provides a mathematical model to predict the dependent variable (GPA) based on the independent variable (SAT score).
2. **A reasonable prediction SAT score of 2100 is a GPA of 3.5.**
- **This statement's correctness depends on the actual data points on the scatter plot.** If the line of best fit at a SAT score of 2100 indeed predicts a GPA around 3.5, then this statement is correct. If not, it may be incorrect.
3. **A reasonable prediction SAT score of 1700 is a GPA of 3.0.**
- **Similar to the previous statement, this depends on the plot.** If the calculated GPA at a SAT score of 1700 is around 3.0 based on the line of best fit, this would be correct, otherwise incorrect.
4. **The line of best fit shows that the SAT score and GPA have a negative association.**
- **Incorrect.** The description states that there is a positive correlation, which means higher SAT scores are associated with higher GPAs, not a negative one.
5. **The line of best fit gives the best approximation of the association between SAT score and GPA.**
- **Correct.** The purpose of the line of best fit is to provide the best linear approximation of the relationship between the two variables.
In summary, the correct statements are:
1. The line of best fit can be used to make predictions of GPA based on SAT score.
5. The line of best fit gives the best approximation of the association between SAT score and GPA.
The correctness of the predictions for SAT scores of 2100 and 1700 without the graph can't be definitively answered here without seeing the actual line of best fit.
1. **The line of best fit can be used to make predictions of GPA based on SAT score.**
- **Correct.** A line of best fit provides a mathematical model to predict the dependent variable (GPA) based on the independent variable (SAT score).
2. **A reasonable prediction SAT score of 2100 is a GPA of 3.5.**
- **This statement's correctness depends on the actual data points on the scatter plot.** If the line of best fit at a SAT score of 2100 indeed predicts a GPA around 3.5, then this statement is correct. If not, it may be incorrect.
3. **A reasonable prediction SAT score of 1700 is a GPA of 3.0.**
- **Similar to the previous statement, this depends on the plot.** If the calculated GPA at a SAT score of 1700 is around 3.0 based on the line of best fit, this would be correct, otherwise incorrect.
4. **The line of best fit shows that the SAT score and GPA have a negative association.**
- **Incorrect.** The description states that there is a positive correlation, which means higher SAT scores are associated with higher GPAs, not a negative one.
5. **The line of best fit gives the best approximation of the association between SAT score and GPA.**
- **Correct.** The purpose of the line of best fit is to provide the best linear approximation of the relationship between the two variables.
In summary, the correct statements are:
1. The line of best fit can be used to make predictions of GPA based on SAT score.
5. The line of best fit gives the best approximation of the association between SAT score and GPA.
The correctness of the predictions for SAT scores of 2100 and 1700 without the graph can't be definitively answered here without seeing the actual line of best fit.