Without seeing the actual scatter plot or the line of best fit, I cannot provide specific answers regarding the accuracy of the given predictions for the SAT scores of 1700 and 2100. However, I can confirm the general accuracy of the other statements about lines of best fit:
- "The line of best fit gives the best approximation of the association between SAT score and GPA." This statement is typically correct. The line of best fit, also known as the regression line, is a statistical tool used to approximate the relationship between two quantitative variables.
- "This is not an accurate line of best fit because it doesn't hit the lowest point." This statement is a misconception. The line of best fit is not necessarily expected to pass through the lowest or highest points in a scatter plot. It is meant to minimize the overall distance between the line and all the points in the data set, capturing the central tendency of the relationship.
- "The line of best fit can be used to make predictions of GPA based on SAT score." This is generally correct. Once a line of best fit is established, it can be used to predict the value of one variable based on the known value of the other.
- "The line of best fit shows that the combined SAT Score and first semester SAT have a negative correlation." This statement can only be confirmed if it is clear from the scatter plot that the slope of the line of best fit is negative. If the SAT scores increase while GPAs decrease, that would indicate a negative correlation. But if the SAT scores and GPAs both tend to increase together, then they have a positive correlation. This needs to be checked against the actual data.
For the predictions:
- "A reasonable prediction SAT score of 1700 is a GPA of 3.0." Whether this is a reasonable prediction would depend on the actual line of best fit in the scatter plot.
- "A reasonable prediction SAT score of 2100 is a GPA of 3.5." Similarly, this prediction's reasonableness would depend on the scatter plot's specific trend and the line of best fit's slope.
I would need to see the actual scatter plot and have some more context to give a definitive answer on the predictions about specific SAT scores and corresponding GPAs.
The scatter plot shows the relationship between combined SAT score and first semester college GPA.
Choose all statements that are correct?
(3 points)
Responses
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 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.
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 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.
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.
A reasonable prediction SAT score of 2100 is a GPA of 3.5.
1 answer