Variation, Direct and Inverse | index-art.info
I have gotten several different and conflicting definitions from A direct relationship would be one in which all x's increase as y increases. Definition of indirect relationship: The relationship between two variables which interface with group 2, but neither of them interfaces directly with each other. Two types of relationships between variables are direct and inverse variation. In general, direct variation suggests that two variables change in the same.
Consider the relationship between price of a good or service and quantity demanded.
Variation, Direct and Inverse
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.
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. 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.
What is an indirect relationship? Definition and examples
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.Direct and inverse proportions(Direct proportion-01)
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.
Inverse or Indirect? - Mathematics - Science Forums
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. This creates an indirect relationship. Inverse relationship An inverse relationship, negative correlation, or inverse correlation is a contrary relationship between two variables.
In other words, the two variables move in opposite directions. For example, if Group 1 moves up, Group 2 subsequently declines, and vice-versa.
Whether there is another variable in the situation is irrelevant. In other words, inverse relationships may be either indirect or direct relationships. There may be three or just two variables present. It reported last week that the sales of diet products had increased. At the same time, sales of candy and chocolate had declined. Sometimes, it happened the other way round.
Interest rates and the inflation rate have an inverse relationship. Inverse Variation When two variables vary inversely, one increases as the other decreases. As one variable is multiplied by a given factor, the other variable is divided by that factor, which is, of course, equivalent to being multiplied by the reciprocal the multiplicative inverse of the factor.
For example, if one variable doubles, the other is divided by two multiplied by one-half ; if one triples, the other is divided by three multiplied by one-third ; if one is multiplied by two-thirds, the other is divided by two-thirds multiplied by three-halves.
Consider a situation in which miles are traveled. If traveling at an average rate of 5 miles per hour mphthe trip takes 20 hours. If the average rate is doubled to 10 mph, then the trip time is halved to 10 hours. If the rate is doubled again, to 20 mph, the trip time is again halved, this time to 5 hours. If the average rate of speed is 60 mph, this is triple 20 mph.
Therefore, if it takes 5 hours at 20 mph, 5 is divided by 3 to find the travel time at 60 mph. In general, variables that vary inversely can be expressed in the following forms: The graph of the relationship between quantities that vary inversely is one branch of a hyperbola. See part b of the figure. The graph is asymptotic to both the positive x -and y -axes.