Slope and Marginal Values
Looking at the Grades and Hours
Studied Example
Chpt. 2
A-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
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)
5
Grade
4
3
grade
2
1
0
0
5
10
15
20
25
Hours Studied
30
35
Actual Data Versus Predicted
Actual and Predicted Grade
5
Grade
4
3
Grade
2
Predicted
1
0
5
5 10 13 15 18 19 25 26 31 35
Hours Studied
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 (slope)
– Takes 35 hours of studying to get a 4.0
A Demand Curve
• Qd = F(Px, Psub, Pcompl, Inc)
– Qd = a - b*Px + c*Ps – d* Pc +/- e*Inc
•
•
•
•
b always negative (First law of demand)
c always positive (substitute)
d always negative (complement – consumed with)
e positive or negative -> “normal” or “inferior” good
System of Equations
• At equilibrium
– Price sellers charge = price consumers pay
(P*)
– Quantity produced by sellers = quantity
demanded by consumers
– P* is the price that simultaneously solves for
equilibrium – and it is unique (only 1 P*)
• Qd = a – b*P(*)
• Qs = c + b*P(*)