Question

What is b when sy = 25.3, sx = 45.7, and r = 0.98? Answer choices: a. b = 1.770 b. b = 0.554 c. b = 1.806 d. b = 0.039 e. b = 0.543

Answer 1

The value of b is approximately 0.543 when calculated using the given standard deviations and correlation coefficient.

Step-by-step explanation:

The calculation of b (the slope of the regression line) in statistics uses the formula b = r(sy/sx), where r is the correlation coefficient, sy is the standard deviation of the Y values, and sx is the standard deviation of the X values. Given, sy = 25.3, sx = 45.7, and r = 0.98, we can substitute these into the formula:
b = 0.98 (25.3/45.7)
After performing the calculation:
b = 0.98 * 0.5536
b ≈ 0.5425, which is approximately 0.543 when rounded to three decimal places.