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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

Appendix Chapter 1

WORKING WITH GRAPHS

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

Run in X

2 slope cont1
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 cont2
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
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
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
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
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.