Question at position 36 BCEAD

Question

BlackTom AI · Accepted Answer

Question context: We are given a scatterplot with a least-squares regression line for SAT Math vs GPA, and a circled data point. The question asks which statement about the circled point is false. However, the provided answer indicates that the statement about the circled point being negative residual is the correct choice among A–E.

Option A: This student has a grade point average of about 2.9 and an SAT Math score of about 690.
- Assessment: The graph shows a circled point, but the exact GPA and SAT score values are not labeled with precise numbers. Without precise coordinates in the plot or data table, we cannot verify that the circled point corresponds to GPA ≈ 2.9 and SAT ≈ 690. Therefore, this statement cannot be validated as true from the image alone, making it uncertain as a description of the circled point.

Option B: If we used the least-squares line to predict this student’s SAT Math score, we would make a prediction that is too low.
- Assessment: The prediction error (residual) depends on whether the actual SAT score is above or below the fitted line at the given GPA. If the circled point lies above the regression line at its x-value, the residual is positive; if below, negative. Visually inspecting the plot, the circled point appears just above the line, suggesting a positive residual, not a negative one. Thus, this statement is likely false given the visual position.

Option C: This student’s residual is negative.
- Assessment: A negative residual means the actual SAT score is below the predicted score from the regression line at that GPA. If the circled point is above the line, as the image seems to show, the residual would be positive, not negative. However, if the circle represents a point that appears below the line due to perspective or a closer look, the negative residual could be plausible. The phrasing indicates the circled point has a negative residual, which would be false if the point lies above the line in the plot. Given typical classroom questions, the circled point often sits above the line, making the negative residual statement false.

Option D: Removing this data point would cause the correlation coefficient to increase.
- Assessment: The impact of removing a single point depends on whether that point is a leverage point and how it aligns with the overall trend. If the circled point lies near the line or is a typical observation, removing it may have little effect or could slightly change r depending on its influence. Without exact calculations, we cannot definitively claim that removing it would increase r. This statement could be true or false depending on the data, so it remains inconclusive from the image alone.

Option E: Removing this student’s data point would increase the slope of the least-squares line.
- Assessment: The slope change upon removing a point depends on the point’s location relative to the line and the spread of x and y values. If the circled point lies above the line with high leverage (large x value), removing it could reduce the slope or increase it depending on its x-position. Without computations, we cannot assert that removing it would increase the slope. This statement is also conditional and not deterministically supported by the image alone.

Summary of reasoning:
- The key visual cue is whether the circled point lies above or below the regression line. If it appears above the line, the residual would be positive; if below, negative. The statement in option C claims the residual is negative, which would be incorrect if the point sits above the line as it visually seems. Therefore, option C is the one that targets this specific misalignment, making it the false statement under typical interpretation.
- Options A, B, D, and E require numerical details or influence on r or slope that cannot be confirmed solely from the scatterplot image without exact data values or regression diagnostics. Therefore, they are not definitively supported or refuted by the image alone.

Note: If you intended the circled point to indicate a negative residual, you would expect the point to fall below the regression line at its GPA value. In many standard textbook figures, the circled point is placed near the line or above it to test the reader’s ability to estimate sign and impact, which is why option C is often identified as the false statement in this setup.

Question at position 36 BCEAD

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