1. Slope and Marginal Values Looking at the Grades and Hours Studied Example Chpt. 2

2. Using the coordinate system A-2 2 Grade point average is measured on the vertical axis and study time on the horizontal axis. Albert E., Alfred E., and their classmates are represented by various points. We can see from the graph that students who study more tend to get higher grades.

3. Using Regression Analysis Want to find the linear equation that best fits the data –Y = a + b*X (general form) –Grade = a + b* Hours_Studied A = intercept (= grade without studying) B = slope (= increase in grade with each additional hour of study)

4. Data and Results GradeStudy Hours slope0.0546782.086814 25 std err0.0100760.208639 2.85 R^20.7659030.319685 2.410 F29.445679 2.913 2.415 3.318 3.519 3.525 3.726 3.631 3.935

5. Graphically

6. Actual Data Versus Predicted

7. Marginal Benefits of Studying Grade = 2.1 + 0.055 * Hours Studied Interpretation –Expected grade without studying = 2.1 Marginal benefits of studying –Each additional hour of studying raises your grade by.055 –Takes 35 hours of studying to get a 4.0