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Appendix Chapter 1 WORKING WITH GRAPHS

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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

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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.

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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 Y over 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

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

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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.

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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.

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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

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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.

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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 and high 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.

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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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