Direct and inverse relationships - Math Central
Definition of direct relationship: A relationship between two numbers or other variables where an increase or decrease in one variable causes the same. The relationship between two variables is a direct relationship if when one increases so does the other or as one decreases so does the other. The radius of a. 1. descriptions of how two variables relate to each other on a graph. 2. usually A direct relationship is when one variable increases, so does the other.
We would choose an appropriate scale for the rate of inflation on the y vertical axis; and on the x horizontal axis show the ten years from to with on the left, and on the right. We would notice right away a trend. The trend in the inflation rate data is a decline, actually from a high of 5. We would see that there has been some increase in the inflation rate since its absolute low inbut not anything like the high.
And, if we did such graphs for each of the decades in Canada sincewe would see that the s were a unique decade in terms of inflation.
No decade, except the s, shows any resemblance to the s. We can then discuss the trends meaningfully, since we have ideas about the data over a major period of time. We can link the data with historical events such as government anti-inflation policies, and try to establish some connections. Other graphs are used to present a relationship between two variables, or in some instances, among more than two variables. Consider the relationship between price of a good or service and quantity demanded.
The two variables move in opposite directions, and therefore demonstrate a negative or indirect relationship. Aggregate demand, the relationship between the total quantity of goods and services demanded in the entire economy, and the price level, also exhibits this inverse or negative relationship.
If the price level based on the prices of a given base year rises, real GDP shrinks; while if the price level falls, real GDP increases.
Direct and Inverse Relationships
Further, the supply curve for many goods and services exhibits a positive or direct relationship. The supply curve shows that when prices are high, producers or service providers are prepared to provide more goods or services to the market; and when prices are low, service providers and producers are interested in providing fewer goods or services to the market. The aggregate expenditure, or supply, curve for the entire Canadian economy the sum of consumption, investment, government expenditure and the calculation of exports minus imports also shows this positive or direct relationship.
Construction of a Graph You will at times be asked to construct a graph, most likely on tests and exams. You should always give close attention to creating an origin, the point 0, at which the axes start. Label the axes or number lines properly, so that the reader knows what you are trying to measure.
- Direct Proportion and The Straight Line Graph
Most of the graphs used in economics have, a horizontal number line or x-axis, with negative numbers on the left of the point of origin or 0, and positive numbers on the right of the origin. Figure 2 presents a typical horizontal number line or x-axis. In economics graphs, you will also find a vertical number line or y-axis. Here numbers above the point of origin 0 will have a positive value; while numbers below 0 will have a negative value.
Figure 3 demonstrates a typical vertical number line or y-axis. When constructing a graph, be careful in developing your scale, the difference between the numbers on the axes, and the relative numbers on each axis. The scale needs to be graduated or drawn properly on both axes, meaning that the distance between units has to be identical on both, though the numbers represented on the lines may vary.
You may want to use single digits, for example, on the y-axis, while using hundreds of billions on the x-axis. Using a misleading scale by squeezing or stretching the scale unfairly, rather than creating identical distances for spaces along the axes, and using a successive series of numbers will create an erroneous impression of relationship for your reader.
If you are asked to construct graphs, and to show a knowledge of graphing by choosing variables yourself, choose carefully what you decide to study.
Here is a good example of a difficulty to avoid. Could you, for example, show a graphical relationship between good looks and high intelligence?
I don't think so. First of all, you would have a tough time quantifying good looks though some social science researchers have tried! Intelligence is even harder to quantify, especially given the possible cultural bias to most of our exams and tests.
Finally, I doubt if you could ever find a connection between the two variables; there may not be any. Choose variables that are quantifiable. Height and weight, caloric intake and weight, weight and blood pressure, are excellent personal examples. The supply and demand for oil in Canada, the Canadian interest rate and planned aggregate expenditure, and the Canadian inflation rate during the past forty years are all quantifiable economic variables.
You also need to understand how to plot sets of coordinate points on the plane of the graph in order to show relationships between two variables. One set of coordinates specify a point on the plane of a graph which is the space above the x-axis, and to the right of the y-axis. For example, when we put together the x and y axes with a common origin, we have a series of x,y values for any set of data which can be plotted by a line which connects the coordinate points all the x,y points on the plane.
Such a point can be expressed inside brackets with x first and y second, or 10,1. A set of such paired observation points on a line or curve which slopes from the lower left of the plane to the upper right would be a positive, direct relationship. A set of paired observation or coordinate points on a line that slopes from the upper left of the plane to the lower right is a negative or indirect relationship.
Working from a Table to a Graph Figures 5 and 6 present us with a table, or a list of related numbers, for two variables, the price of a T-shirt, and the quantity purchased per week in a store. Note the series of paired observation points I through N, which specify the quantity demanded x-axis, reflecting the second column of data in relation to the price y-axis, reflecting first column of data.
See that by plotting each of the paired observation points I through N, and then connecting them with a line or curve, we have a downward sloping line from upper left of the plane to the lower right, a negative or inverse relationship.
We have now illustrated that as price declines, the number of T-shirts demanded or sought increases. Or, we could say reading from the bottom, as the price of T-shirts increases, the quantity demanded decreases.
We have stated here, and illustrated graphically, the Law of Demand in economics. Now we can turn to the Law of Supply. The positive relationship of supply is aptly illustrated in the table and graph of Figure 7.
Note from the first two columns of the table that as the price of shoes increases, shoe producers are prepared to provide more and more goods to this market. The converse also applies, as the price that consumers are willing to pay for a pair of shoes declines, the less interested are shoe producers in providing shoes to this market. The x,y points are specified as A through to E. When the five points are transferred to the graph, we have a curve that slopes from the lower left of the plane to the upper right.
We have illustrated that supply involves a positive relationship between price and quantity supplied, and we have elaborated the Law of Supply. Now, you should have a good grasp of the fundamental graphing operations necessary to understand the basics of microeconomics, and certain topics in macroeconomics.
Types of Relationships
Many other macroeconomics variables can be expressed in graph form such as the price level and real GDP demanded, average wage rates and real GDP, inflation rates and real GDP, and the price of oil and the demand for, or supply of, the product.
Don't worry if at first you don't understand a graph when you look at it in your text; some involve more complicated relationships. You will understand a relationship more fully when you study the tabular data that often accompanies the graph as shown in Figures 5 and 7or the material in which the author elaborates on the variables and relationships being studied. Gentle Slopes When you have been out running or jogging, have you ever tried, at your starting pace, to run up a steep hill?
At least, I hope not. While there is a relationship between the number of roads built and the number of babies, we don't believe that the relationship is a causal one. This leads to consideration of what is often termed the third variable problem. In this example, it may be that there is a third variable that is causing both the building of roads and the birthrate, that is causing the correlation we observe.
For instance, perhaps the general world economy is responsible for both. When the economy is good more roads are built in Europe and more children are born in the U. The key lesson here is that you have to be careful when you interpret correlations. If you observe a correlation between the number of hours students use the computer to study and their grade point averages with high computer users getting higher gradesyou cannot assume that the relationship is causal: In this case, the third variable might be socioeconomic status -- richer students who have greater resources at their disposal tend to both use computers and do better in their grades.
It's the resources that drives both use and grades, not computer use that causes the change in the grade point average. Patterns of Relationships We have several terms to describe the major different types of patterns one might find in a relationship.
First, there is the case of no relationship at all. If you know the values on one variable, you don't know anything about the values on the other. For instance, I suspect that there is no relationship between the length of the lifeline on your hand and your grade point average. Then, we have the positive relationship. In a positive relationship, high values on one variable are associated with high values on the other and low values on one are associated with low values on the other.
In this example, we assume an idealized positive relationship between years of education and the salary one might expect to be making. On the other hand a negative relationship implies that high values on one variable are associated with low values on the other.