Question

The calculator screen shows the linear regression for the data in the table.
What type of correlation does the correlation coefficient indicate, and why?

Calculator screen shot of Lin Reg. The equation is y equals a x plus b, where a equals negative 1.96341463 and b equals 19.09756098. The r squared value is point 9 8 1 7 0 7 3 1 7 1 and the r value is negative point 9 9 0 8 1 1 4 4 3 8.

x 1 3 4 5 6 8 9
y 17 12 12 10 8 3 1
A. a strong positive correlation; r2 ≈ 1
B. a weak positive correlation; r < 1
C. a strong negative correlation; r ≈ –1
D. a weak negative correlation; r2 < 1

Answer 1

C. a strong negative correlation; r ≈ –1

Reason: r ≈ –0.9908 is very close to –1, indicating a strong negative linear relationship (the slope is negative and y decreases as x increases). Although r^2 ≈ 0.9817 is near 1 (showing a strong fit), the sign of r (negative) gives the direction.