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

Choose THREE 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.

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.

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 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.

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

1 answer

Based on your descriptions, here are the three correct statements:

  1. The line of best fit gives the best approximation of the association between SAT score and GPA.
    This statement is correct because the line of best fit is designed to represent the overall trend or relationship in the data.

  2. A reasonable prediction SAT score of 1700 is a GPA of 3.0.
    This statement may or may not be correct, depending on the specific data points and the line of best fit shown in the scatter plot. Without the actual plot, I cannot verify it, but it could potentially be one of the correct statements if the line of best fit supports that prediction.

  3. The line of best fit can be used to make predictions of GPA based on SAT score.
    This is correct, as the line of best fit is often used to estimate y-values (in this case, GPA) based on x-values (SAT scores).

The other statements can be rejected for various reasons:

  • The line of best fit reflecting a "negative correlation" would suggest that higher SAT scores correspond to lower GPAs, which is typically not the case in academic performance contexts.
  • The prediction of a GPA of 3.5 for an SAT score of 2100 would need to be verified against the data, and without visual confirmation, its accuracy cannot be guaranteed.
  • The last statement about the line of best fit not being accurate because it "doesn't hit the lowest point" is generally irrelevant, as the line of best fit doesn't need to pass through every point or even the lowest point; its purpose is to capture the general trend.

Thus, the most confident selections would be statements 1, 2 (if supported by the plot), and 4.