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

2. Using the coordinate system
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. 2

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 Grade Study Hours slope 0.054678 2.086814 2 5 std err
2.8
R^2
2.4 10 F 9
2.9 13 15
3.3 18
3.5 19 25
3.7 26
3.6 31
3.9 35

5. Graphically

6. Actual Data Versus Predicted

7. Marginal Benefits of Studying
Grade = * 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