Appendix Chapter 1

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Appendix Chapter 1. WORKING WITH GRAPHS. 1. Positive and Negative Relationships. Graphs reveal a positive or negative relationship.

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Appendix Chapter 1

WORKING WITH GRAPHS

1. Positive and Negative Relationships
• Graphs reveal a positive or negative relationship.
• A positive relationship (or direct relationship) exists between two variables if an increase in the value of one variable is associated with an increase in the value of the other variable.
• Two positively related variables are graphed as an upward-sloping curve.
• See graph for upward-sloping curve
1. Positive and Negative Relationships – cont.
• A negative relationship (or inverse relationship) exists if an increase in the value of one variable leads to a reduction in the value of the other.
• When two variables are negative related, the graph of the relationship is a downward-sloping curve.
• See graph for downward-sloping curve.
• If there is a change in relationships the entire graph can shift, left or right.
2. Slope
• The relationship between two variable can be represented by a curve’s slope.
• The slope of a straight line is defined as the ratio of the rise (or fall) in Yover the run in X.
• A positive value of the slope signifies a positive relationship between the two variables.
• Slope = Rise in Y

Run in X

2. Slope – cont.
• A negative value of the slope signifies a negative relationship.
• Slope = Fall in Y

Run in X

2. Slope – cont.
• Formula for positive relationship or negative relationship.
• Slope = Y

X

• Delta Y (or X) or Y (or X) stand for the change in the value.
2. Slope – cont.
• A linear relationship is the connected points with a straight line.
• In a curvilinear relationship the slope change, there is thus no single slope of a curvilinear relationship.
• A tangent is a straight line that touches the curve at only one point.
• See graph for calculating slopes of curvilinear relationships.
• Economists pay considerable attention to the minimum and maximum values of relationships, see graph.
3. Areas
• The area of a rectangle = multiply the height of the rectangle by the width of the rectangle.
• The area of a triangle = area of the rectangle x ½
4. Relationships, Trends, and Scattered Diagrams
• Much of economics is about relationships among economic variables.
• Most economics are measured over time.
• A time series is a measurement of one or more variables over a designated period of time, such as months, years, or quarters.
4.1 Scatter diagram
• A scatter diagram plots the values of one variable against the values of another for a specific time interval.
• If the dots show a pattern of low prices andhigh usage but high prices and low usage, the scatter diagram suggest a negative relationship, indicating by a general declining pattern of dots from left to right.
• A general rising pattern of dots from left to right shows a positive relationship.
• If there were no relationship, the dots would be randomly.
4.2 Time trend
• A time trend is the tendency of variables to rise generally, or to fall generally, with the general rise in economy.
• Time trends make it difficult to determine whether two variables are really related or are simply reacting to common trends.
• By working with first differences, we remove time trends and are in a better position to determine whether the relationship is truly positive or negative.
• Outliers are located far from the trend lines. Outliers suggest that some extraordinary event occurred often in that year that affected the outcome.