In statistics, a perfect positive correlation is represented by 1, while 0 indicates no correlation, and negative 1 indicates a perfect negative. Differentiate between a positive relationship and a negative relationship useful in economics, because it measures the relationship between two variables. the total amount produced, you expect to find. A) a positive trend. B) no relationship between time and the amount produced. C) an inverse relationship between.
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. 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!
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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.
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? If so, you will have a good intuitive grasp of the meaning of a slope of a line.
You probably noticed your lungs starting to work much harder to provide you with extra oxygen for the blood. If you stopped to take your pulse, you would have found that your heart is pumping blood far faster through the body, probably at least twice as fast as your regular, resting rate. The greater the steepness of the slope, the greater the sensitivity and reaction of your body's heart and lungs to the extra work. Slope has a lot to do with the sensitivity of variables to each other, since slope measures the response of one variable when there is a change in the other.
The slope of a line is measured by units of rise on the vertical y-axis over units of run on the horizontal x-axis. A typical slope calculation is needed if you want to measure the reaction of consumers or producers to a change in the price of a product. For example, let's look at what happens in Figure 7 when we move from points E to D, and then from points B to A. The run or horizontal movement is 80, calculated from the difference between and 80, which is Let's look at the change between B and A.
The vertical difference is again 20 - 80while the horizontal difference is 80 - We can generalize to say that where the curve is a straight line, the slope will be a constant at all points on the curve. Figure 8 shows that where right-angled triangles are drawn to the curve, the slopes are all constant, and positive. Now, let's take a look at Figure 9, which shows the curve of a negative relationship. All slopes in a negative relationship have a negative value.Introduction to Relationships in a Principles of Economics Class
We can generalize to say that for negative relationships, increases in one variable are associated with decreases in the other, and slope calculations will, therefore, be of a negative value. A final word on non-linear slopes. Variables are inversely related if they move in opposite directions.
Both covariance and correlation indicate whether variables are positively or inversely related. Correlation also tells you the degree to which the variables tend to move together.
You are probably already familiar with statements about covariance and correlation that appear in the news almost daily.
For example, you might hear that as economic growth increases, stock market returns tend to increase as well. These variables are said to be positively related because they move in the same direction.
You may also hear that as world oil production increases, gasoline prices fall. These variables are said to be negatively, or inversely, related because they move in opposite directions. The relationship between two variables can be illustrated in a graph. In the examples below, the graph on the left illustrates how the positive relationship between economic growth and market returns might appear.
The graph indicates that as economic growth increases, stock market returns also increase. The graph on the right is an example of how the inverse relationship between oil production and gasoline prices might appear. It illustrates that as oil production increases, gas prices fall. To determine the actual relationships of these variables, you would use the formulas for covariance and correlation.
Covariance Covariance indicates how two variables are related. A positive covariance means the variables are positively related, while a negative covariance means the variables are inversely related.
The formula for calculating covariance of sample data is shown below. Before you compute the covariance, calculate the mean of x and y. The Summary Measures topic of the Discrete Probability Distributions section explains the mean formula in detail.
Negative relationship - Wikipedia
Now you can identify the variables for the covariance formula as follows. Since the covariance is positive, the variables are positively related—they move together in the same direction. Correlation Correlation is another way to determine how two variables are related.
In addition to telling you whether variables are positively or inversely related, correlation also tells you the degree to which the variables tend to move together. As stated above, covariance measures variables that have different units of measurement.
Using covariance, you could determine whether units were increasing or decreasing, but it was impossible to measure the degree to which the variables moved together because covariance does not use one standard unit of measurement.
To measure the degree to which variables move together, you must use correlation. Correlation standardizes the measure of interdependence between two variables and, consequently, tells you how closely the two variables move. The correlation measurement, called a correlation coefficient, will always take on a value between 1 and — 1: