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Appendix Chapter 1

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

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  1. Appendix Chapter 1 WORKING WITH GRAPHS

  2. 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

  3. 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.

  4. 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

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

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

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