1D. Graphs
Two-Variable
Relationship (Part 1)
Slope (Part 1A –
Section 1)
- The slope of a
line or curve is a measure of how steep it is. The slope of a line is measured by “rise over run” – the change in the
y-variable between two points on the line divided by the change in the
x-variable between those two points.
Positive and Negative Linear Relationship (Part 1A – Section 2)
- Two variables have a positive
relationship when an increase in the value of one variable is associated
with an increase in the value of the other variable. It is illustrated by a
curve that slopes upward from left to right.
- Two variable has a negative
relationship when an increase in the value of one variable is associated
with a decrease in the value of the other variable. It is illustrated by a
curve that slopes downward from left to right.
Zero Linear
Relationship (Part 1A – Section 3)
- The horizontal intercept
(zero slope) of a curve is the point
at which it hits the horizontal axis; it indicates the value of the y-variable
when the value of the x-variable is zero.
- The vertical
intercept (infinite slope) of a
curve is the point at which it hits the vertical axis; it shows the value of
y-variable when the value of the x-variable is zero.
Infinity Linear
Relationship (Part 1A – Section 4)
- An infinite slope
is a vertical line.
- When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis.
Nonlinear Curve (Part
1B- Section 1)
- A nonlinear curve
is one in which the slope is not the same between every pair of points.
Positive and Negative Nonlinear
Curves (Part 1B - Section 2)
- A positive
increasing slope is a curve that is upward sloping and gets steeper.
(Concave Up, Slopes Increasing)
- A positive
decreasing slope is a curve that is upward sloping but gets flatter.
(Concave Down, Slopes Decreasing)
- The absolute value of
a negative number is the value of
the negative number without the
minus sign.
- Negative increasing
slope is when the absolute value of the slope steadily increases as you
move from left to right. (Concave Up, Slopes Increasing)
- Negative decreasing
slope is when the absolute value of the slope steadily decreases along the
curve. (Concave Down, Slopes Decreasing)
Maximum and Minimum
Points (Part 1B – Section 3)
- A nonlinear curve may have a maximum point, the highest point along the curve. At the maximum,
the slope of the curve changes from positive to negative.
- A nonlinear curve may have a minimum point, the lowest point along the curve. At the minimum, the slope of the curve changes
from negative to positive.
- An arc of a
curve is some piece or segment of that curve.
Reverse Causality
(Part 1C)
- The error of reverse
causality is committed when the true direction of causality between two
variables are reversed.
Multiple-Variable
Relationship (Part 2)
Correlation Is Not
Causation (Part 2A)
- An omitted variable
is an unobserved variable that, though its influence on other variables,
creates the erroneous appearance of a direct causal relationship among those
variables.
Other-Things-Being-Equal
Assumption (Part 2B)
- The other things
equal assumption means that all other relevant factors remain unchanged.
Two-Dimensional Graph
(Part 2C)
- In a causal relationship, the determining variable is
called the independent variable.
- In a causal relationship, the variable it determines is
called the dependent variable.
- If the curve is a straight line, the variables have a linear relationship.
- If the curve is not a straight line, the variables have a nonlinear relationship.