Transcript TOOLS USED TO EXPRESS RELATIONSHIPS

TOOLS USED TO EXPRESS
RELATIONSHIPS
Schedules
Graphs
Equations
Schedule ( or Table)

Definition:

a list of different
values of a variable
and the value of a
related variable
Price
$2
4
6
8
Quantity
20
15
10
5
Equation

Definition:


a mathematical statement usually involving
dependent and independent variables.
Example:

Qd = f(P)

Dependent variable:


a variable that changes as the controlled
variable is changed
Independent variable:


the controlled variable
a variable that is not a function of the
equation and causes change in the
dependent variable
Graph

Definition:


a visual
representation of
functional
relationships or the
movements of a
variable over time.
Purpose

to visualize the
relationship
P
D
Q
Constructing a Graph

Step 1: Number line
Y
Positive Y
Negative X
Positive Y
Positive X
0
X
0
Negative Y
Negative X
Negative Y
Positive X
Constructing a Graph
Step 1: Number line
0
5
Do this…
10
20
15
25
NOT this…
0
5
20
30
52
55
70 72
Constructing a Graph

Step 2: Label axis
Price
Quantity
Constructing a Graph

Step 2: Plot Points on graph
Price
..
.
Quantity
Constructing a Graph

Step 3: Connect Points on graph
Price
..
.
Quantity
Constructing a Graph

Step 4: Label Lines
Price
..
.
Demand
Quantity
Linear Relationships between
Variables
Negative
Relationship
also called:
Inverse or Indirect
Relationship


as values of X
change, values of Y
change in the
opposite direction
Y
Y = f(X)
X
Linear Relationships between
Variables

Positive Relationship
also called:
Direct Relationship

as values of X
change, values of Y
change in the same
direction
Y
Y = f(X)
X
Measuring Linear
Relationships

Slope

measures how
strongly the
dependent variable is
influenced by the
independent variable

Formula
Slope = Rise / Run
= Change in Y
Change in X
Measuring Linear
Relationships

Negative lines have
negative slopes

Positive lines have
positive slopes

Straight lines have
only one slope along
the line.

Intercept:

the value of the dependent variable (Y)
when the value of the independent variable
(X) is zero
Y
Y = f(X)
intercept
X
Graphical Assumptions

Homogeneous Units


each unit of the independent variable (X) is
identical
Divisibility

each unit of the independent variable can
be divided infinitesimally
Nonlinear Relationships


Exhibit changing
relationship between
variables
Y
Y = f(X)
Have more than one
slope along the line
X
Nonlinear relationships

At the minimum
point the slope is
equal to zero

At the maximum
point the slope is
equal to zero
Nonlinear Relationships

Four types:
1.
Increasing at an increasing rate
2.
Increasing at a decreasing rate
3.
Decreasing at a decreasing rate
4.
Decreasing at an increasing rate
Nonlinear relationship

Increasing at an
Increasing Rate:

Y
Y = f(X)
increases in the X
variable lead to
larger increases in
the Y Variable
X
Nonlinear relationship

Increasing at a
Decreasing Rate:

Y
Y = f(X)
increases in the X
variable lead to
smaller increases in
the Y Variable
X
Nonlinear relationship

Decreasing at a
Decreasing Rate:

increases in the X
variable lead to
smaller decreases in
the Y Variable
Y
Y = f(X)
X
Nonlinear relationship

Decreasing at an
Increasing Rate:

increases in the X
variable lead to
larger decreases in
the Y Variable
Y
Y = f(X)
X