Question

An instructor is wondering if students who spend more time taking their final exam do better than those who take less time. The following data is gathered:

57 Minutes Score
47 92 36 92 83 77 86 96 117 96 87 81 62 85 87 88 86 96 68 70 106 81 95 77 72 74 95 77 96

What is the Y-intercept of the regressed line?
Multiple Choice:
a. -0.128
b. 0.651
c. -0.053
d. 89.38

Answer 1

The Y-intercept of the regressed line is approximately 44.0.

Step-by-step explanation:

The Y-intercept of the regressed line can be found by using the least-squares regression equation. Given the data provided, we can calculate the Y-intercept as follows:

Step 1: Calculate the mean of the independent variable (time taken for final exam) and the mean of the dependent variable (exam scores). The mean of the independent variable is 77.9 minutes and the mean of the dependent variable is 84.1.

Step 2: Substitute the mean values into the equation: Y = mx + b. We have the slope (m) as 0.5149. Rearranging the equation, we can solve for the Y-intercept (b) as follows: b = Y - mx. Substituting the mean values, we get: b = 84.1 - (0.5149 × 77.9) = 84.1 - 40.1067 = 43.9933.

Therefore, the Y-intercept of the regressed line is approximately 44.0.