The scatter plot shows the relationship between combined SAT score and first semester college GPA.

Question

Choose all statements that are correct.

(3 points)
Responses

The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.
The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.

This is not an accurate line of best fit because it doesn't hit the lowest point.
This is not an accurate line of best fit because it doesn't hit the lowest point.

The line of best fit gives the best approximation of the association between SAT score and GPA.
The line of best fit gives the best approximation of the association between SAT score and GPA.

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 1700 is a GPA of 3.0.
A reasonable prediction SAT score of 1700 is a GPA of 3.0.

A reasonable prediction SAT score of 2100 is a GPA of 3.5.

Answer 1

To assess the accuracy of the statements, let's analyze them one by one based on typical scatter plot interpretations involving SAT scores and college GPA.

1. The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation.

   • Incorrect: Typically, higher SAT scores are associated with higher GPAs, which suggests a positive correlation.

2. This is not an accurate line of best fit because it doesn't hit the lowest point.

   • Incorrect: A line of best fit does not need to touch all data points, including the lowest one. It aims to capture the overall trend of the data.

3. The line of best fit gives the best approximation of the association between SAT score and GPA.

   • Correct: The line of best fit is designed to represent the overall trend in the data, making this statement accurate.

4. The line of best fit can be used to make predictions of GPA based on SAT score.

   • Correct: The line of best fit is indeed used for predicting values based on established trends.

5. A reasonable prediction SAT score of 1700 is a GPA of 3.0.

   • Cannot determine without additional data: This could be true or false depending on the actual placement of the line of best fit on the scatter plot.

6. A reasonable prediction SAT score of 2100 is a GPA of 3.5.

   • Cannot determine without additional data: Similar to the previous statement, this may be accurate or not based on where the line of best fit lies.

Based on this analysis, the correct statements are:

• The line of best fit gives the best approximation of the association between SAT score and GPA.
• The line of best fit can be used to make predictions of GPA based on SAT score.

The correctness of the SAT score predictions (1700 predicting a GPA of 3.0 and 2100 predicting a GPA of 3.5) cannot be determined without the actual scatter plot for reference.