Understanding Graphs Origin Horizontal axis Vertical axis Graph Functional relation Dependent variable Independent variable

Types of graphs Scatter plot diagram: A graph of the value of one variable against the value of another variable Time-series graph: A graph that measures time on the x-axis and the variable or variables of interest on the y-axis. Cross-section graph: A graph that shows the values of a variable for different groups in the population at a point in time.

Scatter plot diagram Source Money Magazine, Vol. 32, No. 1, January, 2004, pp. 102-103.

Time series graph U.S. Unemployment

Bar chart using cross-sectional data Age and salary of employees at Sasnak, Inc. (salary in thousands) Bar chart using cross-sectional data

Basics of a graph Point a: - 5 units X - 15 units Y Point b: 10 5 20 y Vertical axis Point b: - 10 units X - 5 units Y a b Origin 20 15 10 5 x Horizontal axis

Drawing Graphs Dependent variable Types of relations between variables Depends on the independent variable Types of relations between variables Positive; direct Negative; inverse Independent; unrelated

Schedule and Graph relating distance traveled to hours driven 150 100 50 200 Distance traveled per day (miles) 250 Hours driven per day Distance traveled per day (miles) a b c d e 1 2 3 4 5 50 100 150 200 250 a b c d e 4 3 2 1 Hours driven per day 5 Points a through e depict different combinations of hours driven per day and the corresponding distances traveled. Connecting these points graphs a line.

Slopes of Straight Lines Change in vertical variable For a given increase in horizontal variable Slope = Change in the vertical distance/ Increase in the horizontal distance Slope of a straight line The same value along the line

Alternative slopes for straight lines (a) Positive relation (b) Negative relation 10 15 20 y 10 3 20 y Slope = 5/10 = 0.5 5 Slope = - 7 /10 = - 0.7 10 -7 10 x 20 10 x 20 10

Alternative slopes for straight lines Exhibit 8 (c), (d) Alternative slopes for straight lines (c) No relation: zero slope (d) No relation: infinite slope 10 15 20 y 10 20 y Slope = 10 /0 = ∞ 10 Slope = 0/10 = 0 10 x 20 10 x 10

Slope, Units of Measurement, Marginal Analysis Value of slope Depends on units of measurement Measures marginal effects

Slope depends on the unit of measure (a) Measured in feet (b) Measured in yards 5 $6 Total cost 3 $6 Total cost Slope = 1/1 = 1 Slope = 3/1 = 3 1 3 1 1 Feet of copper tubing 6 5 Yards of copper tubing 2 1 Output is measured in feet of copper tubing. Output is measured in yards. The cost: $1 per foot. Slope is different: copper tubing is measured using different units

The Slopes of Curved Lines Differs along the curve Slope of a curved line at one point Slope of the tangent

Slope at different points on a curved line 30 20 10 40 y The slope of a curved line varies from point to point. A At point a, the slope of the curve is equal to the slope of the tangent A. a At point b, the slope of the curve is equal to the slope of the tangent B. B b 40 30 20 10 x

Curves with both positive and negative slopes Exhibit 11 Curves with both positive and negative slopes Some curves have both positive and negative slopes. y The U-shaped curve has: negative slope to the left of b slope of 0 at point b positive slope to the right of b. a b The hill-shaped curve has: positive slope to the left of a slope of 0 at point a negative slope to the right of a. x

Line Shifts Change assumptions Changed relationship between variables

Shift of line relating distance traveled to hours driven Line T hours driven/day and distance traveled/day average speed = 50 mph 150 100 50 200 Distance traveled per day (miles) 250 d T f T’ Line T’ hours driven/day and distance traveled/day average speed = 40 mph 4 3 2 1 Hours driven per day 5