# Graph that shows a direct relationship between two variables drawn

graph. ◇ Distinguish between linear and non-linear relationships and between relationships To show something in a two-variable graph, Variables. The relationship between two variables is graphed by drawing two axes perpendicular to. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The graph shows a relationship between two variables, x and y. A positive relationship or direct relationship is a relationship between two variables that Draw a curve that shows that the number of tickets sold at Disneyland tickets and . A positive or direct relationship is one in which the two variables (we will . or drawn properly on both axes, meaning that the distance between units has to be on the plane of the graph in order to show relationships between two variables.

They assist learners in grasping fairly quickly key economic relationships. Years of statistical analysis have gone into the small graph you can examine to learn about key forces and trends in the economy. Further, they help your instructor to present data in a way which is small-scale or economical, and establish a relationship, frequently historical, between variables in a certain kind of relationship. They permit learners and instructors to establish quickly the peaks and valleys in data, to establish a trend line, and to discuss the impact of historical events such as policies on the data that we wish to analyze.

Types of Graphs in Economics There are various kinds of graphs used in business and economics that illustrate data. These include pie charts segments are displayed as portions, usually percentages, of a circlescatter diagrams points are connected to establish a trendbar graphs results for each year can be displayed as an upward or downward barand cross section graphs segments of data can be displayed horizontally.

You will deal with some of these in economics, but you will be dealing principally with graphs of the following variety. Certain graphs display data on one variable over a certain period of time. For example, we may want to know how the inflation rate has varied in the Canadian economy from 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. 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.

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. You often see pictures representing numerical information.

These pictures may take the form of graphs that show how a particular variable has changed over time, or charts that show values of a particular variable at a single point in time. We will close our introduction to graphs by looking at both ways of conveying information. Time-Series Graphs One of the most common types of graphs used in economics is called a time-series graph. A time-series graph A graph that shows how the value of a particular variable or variables has changed over some period of time.

One of the variables in a time-series graph is time itself. Time is typically placed on the horizontal axis in time-series graphs. The other axis can represent any variable whose value changes over time. The grid with which these values are plotted is given in Panel b. Time-series graphs are often presented with the vertical axis scaled over a certain range. The result is the same as introducing a break in the vertical axis, as we did in Figure These points are then plotted in Panel b.

To draw a time-series graph, we connect these points, as in Panel c. The values for the U. The points plotted are then connected with a line in Panel c. Scaling the Vertical Axis in Time-Series Graphs The scaling of the vertical axis in time-series graphs can give very different views of economic data. We can make a variable appear to change a great deal, or almost not at all, depending on how we scale the axis. For that reason, it is important to note carefully how the vertical axis in a time-series graph is scaled.

Consider, for example, the issue of whether an increase or decrease in income tax rates has a significant effect on federal government revenues. This became a big issue inwhen President Clinton proposed an increase in income tax rates. The measure was intended to boost federal revenues.

Higher tax rates, they said, would cause some people to scale back their income-earning efforts and thus produce only a small gain—or even a loss—in revenues.

Op-ed essays in The Wall Street Journal, for example, often showed a graph very much like that presented in Panel a of Figure It shows federal revenues as a percentage of gross domestic product GDPa measure of total income in the economy, since Various tax reductions and increases were enacted during that period, but Panel a appears to show they had little effect on federal revenues relative to total income.

Her alternative version of these events does, indeed, suggest that federal receipts have tended to rise and fall with changes in tax policy, as shown in Panel b of Figure Which version is correct?

Both graphs show the same data. It is certainly true that federal revenues, relative to economic activity, have been remarkably stable over the past several decades, as emphasized by the scaling in Panel a. And a small change in the federal share translates into a large amount of tax revenue. It is easy to be misled by time-series graphs.

Large changes can be made to appear trivial and trivial changes to appear large through an artful scaling of the axes. The best advice for a careful consumer of graphical information is to note carefully the range of values shown and then to decide whether the changes are really significant.

Testing Hypotheses with Time-Series Graphs John Maynard Keynes, one of the most famous economists ever, proposed in a hypothesis about total spending for consumer goods in the economy.

He suggested that this spending was positively related to the income households receive. One way to test such a hypothesis is to draw a time-series graph of both variables to see whether they do, in fact, tend to move together. Annual values of consumption and disposable income are plotted for the period — Notice that both variables have tended to move quite closely together. This is consistent with the hypothesis that the two are directly related. Department of Commerce The fact that two variables tend to move together in a time series does not by itself prove that there is a systematic relationship between the two.

Notice the steep decline in the index beginning in October, not unlike the steep decline in October Did the mystery variable contribute to the crash? It would be useful, and certainly profitable, to be able to predict such declines. The mystery variable and stock prices appear to move closely together. Was the plunge in the mystery variable in October responsible for the stock crash? The mystery value is monthly average temperatures in San Juan, Puerto Rico. Attributing the stock crash in to the weather in San Juan would be an example of the fallacy of false cause.

Notice that Figure The left-hand axis shows values of temperature; the right-hand axis shows values for the Dow Jones Industrial Average. Two axes are used here because the two variables, San Juan temperature and the Dow Jones Industrial Average, are scaled in different units. Descriptive Charts We can use a table to show data. HERI conducts a survey of first-year college students throughout the United States and asks what their intended academic majors are.

In the groupings given, economics is included among the social sciences. All three panels present the same information.

Panel a is an example of a table, Panel b is an example of a pie chart, and Panel c is an example of a horizontal bar chart. Percentages shown are for broad academic areas, each of which includes several majors. Panels b and c of Figure Panel b is an example of a pie chart; Panel c gives the data in a bar chart.

The bars in this chart are horizontal; they may also be drawn as vertical. Either type of graph may be used to provide a picture of numeric information. Key Takeaways A time-series graph shows changes in a variable over time; one axis is always measured in units of time.

One use of time-series graphs is to plot the movement of two or more variables together to see if they tend to move together or not. The fact that two variables move together does not prove that changes in one of the variables cause changes in the other. Values of a variable may be illustrated using a table, a pie chart, or a bar chart.

The table in Panel a shows a measure of the inflation rate, the percentage change in the average level of prices below.

Panels b and c provide blank grids. We have already labeled the axes on the grids in Panels b and c. It is up to you to plot the data in Panel a on the grids in Panels b and c. Connect the points you have marked in the grid using straight lines between the points. What relationship do you observe?

Has the inflation rate generally increased or decreased? What can you say about the trend of inflation over the course of the s? Here are the time-series graphs, Panels b and cfor the information in Panel a. The first thing you should notice is that both graphs show that the inflation rate generally declined throughout the s with the exception ofwhen it increased.

The generally downward direction of the curve suggests that the trend of inflation was downward. Notice that in this case we do not say negative, since in this instance it is not the slope of the line that matters.

Rather, inflation itself is still positive as indicated by the fact that all the points are above the origin but is declining. Finally, comparing Panels b and c suggests that the general downward trend in the inflation rate is emphasized less in Panel b than in Panel c. This impression would be emphasized even more if the numbers on the vertical axis were increased in Panel b from 20 to Just as in Figure Decide whether each proposition below demonstrates a positive or negative relationship, and decide which graph you would expect to illustrate each proposition.

In each statement, identify which variable is the independent variable and thus goes on the horizontal axis, and which variable is the dependent variable and goes on the vertical axis. An increase in the poverty rate causes an increase in the crime rate. As the income received by households rises, they purchase fewer beans. As the income received by households rises, they spend more on home entertainment equipment. How can we estimate the slope of a nonlinear curve? After all, the slope of such a curve changes as we travel along it.

We can deal with this problem in two ways. One is to consider two points on the curve and to compute the slope between those two points. Another is to compute the slope of the curve at a single point. When we compute the slope of a curve between two points, we are really computing the slope of a straight line drawn between those two points.

### Nonlinear Relationships and Graphs without Numbers

They are the slopes of the dashed-line segments shown. These dashed segments lie close to the curve, but they clearly are not on the curve. After all, the dashed segments are straight lines. When we compute the slope of a nonlinear curve between two points, we are computing the slope of a straight line between those two points. Here the lines whose slopes are computed are the dashed lines between the pairs of points. Every point on a nonlinear curve has a different slope.

To get a precise measure of the slope of such a curve, we need to consider its slope at a single point. To do that, we draw a line tangent to the curve at that point. A tangent line A straight line that touches, but does not intersect, a nonlinear curve at only one point.

The slope of a tangent line equals the slope of the curve at the point at which the tangent line touches the curve. Consider point D in Panel a of Figure We have drawn a tangent line that just touches the curve showing bread production at this point. It passes through points labeled M and N. The vertical change between these points equals loaves of bread; the horizontal change equals two bakers. The slope of our bread production curve at point D equals the slope of the line tangent to the curve at this point.

In Panel bwe have sketched lines tangent to the curve for loaves of bread produced at points B, D, and F. Notice that these tangent lines get successively flatter, suggesting again that the slope of the curve is falling as we travel up and to the right along it. In Panel athe slope of the tangent line is computed for us: Generally, we will not have the information to compute slopes of tangent lines.

We will use them as in Panel bto observe what happens to the slope of a nonlinear curve as we travel along it.

We see here that the slope falls the tangent lines become flatter as the number of bakers rises. Notice that we have not been given the information we need to compute the slopes of the tangent lines that touch the curve for loaves of bread produced at points B and F. In this text, we will not have occasion to compute the slopes of tangent lines. Either they will be given or we will use them as we did here—to see what is happening to the slopes of nonlinear curves.

In the case of our curve for loaves of bread produced, the fact that the slope of the curve falls as we increase the number of bakers suggests a phenomenon that plays a central role in both microeconomic and macroeconomic analysis.

As we add workers in this case bakersoutput in this case loaves of bread rises, but by smaller and smaller amounts.