Slope and Marginal Values

Looking at the Grades and Hours Studied Example

Chpt. 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.

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)

Data and Results

Grade Study Hours slope 0.054678 2.086814

2 5 std err 0.010076 0.208639

2.8 5 R^2 0.765903 0.319685

2.4 10 F 29.44567 9

2.9 13      

2.4 15      

3.3 18      

3.5 19      

3.5 25      

3.7 26      

3.6 31      

3.9 35      

Graphically

Linear Regression (Equation)

0

1

2

3

4

5

0 5 10 15 20 25 30 35

Hours Studied

Gra

de

grade

Actual Data Versus Predicted

Actual and Predicted Grade

0

1

2

3

4

5

5 5 10 13 15 18 19 25 26 31 35

Hours Studied

Grad

e

Grade

Predicted

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