Question

the table and graph shows the relationship between gpa, x, and sat score, y
which statements are correct?
a the value of r is about 0.90.
b this is a strong positive correlation.
c high gpa scores are not associated with high sat scores.
d the equation y = 437.8x + 439.4 models the data.
e there is not a linear relationship between gpa and sat scores.
(table: gpa (2, 2.5, 2.8, 3, 3.3, 3.5, 3.8, 4) and sat score (1240, 1650, 1600, 1800, 1760, 2100, 2300, 1980); graph: scatter plot with gpa (x-axis: 1.5–4.5) and sat (y-axis: 0–2500))

Explanation:

• Option A: The correlation coefficient \( r \) for a strong positive linear relationship is close to 1. A value around 0.90 is reasonable for a strong positive correlation, so A is correct.
• Option B: The scatter plot shows a general upward trend, indicating a strong positive correlation (as points cluster around an increasing line), so B is correct.
• Option C: The upward trend means high GPA is associated with high SAT scores, so C is incorrect.
• Option D: To check the regression equation \( y = 437.8x + 439.4 \), we can test with \( x = 2 \): \( y = 437.8(2)+439.4 = 875.6 + 439.4 = 1315 \), close to the SAT score 1240 (some variation is expected). For \( x = 4 \): \( y = 437.8(4)+439.4 = 1751.2 + 439.4 = 2190.6 \), close to 1980 (again, variation). The equation is a reasonable linear model, so D is correct.
• Option E: The scatter plot shows a linear trend (points follow an approximate straight line), so E is incorrect.

Answer:

A. The value of \( r \) is about 0.90,
B. This is a strong positive correlation,
D. The equation \( y = 437.8x + 439.4 \) models the data