Values of the Pearson Correlation
Describe what Pearson's correlation measures; Give the symbols for Pearson's correlation in the An r of -1 indicates a perfect negative linear relationship between variables, an r of 0 indicates no A perfect positive linear relationship, r = 1. Explore the relationship between positive and negative correlations. When two variables have a negative correlation, they have an inverse relationship. Negative correlations are indicated by a minus (-) sign in front of the. If the correlation coefficient is negative, it may mean that there is an inverse HI, i do face the issue here, when positive coefficient of one predictor is a result in.
In general people who are good in one may have a greater tendency to be good in the other; those who are poor in one may also tend to be poor in the other. If this relatioship is true, then we can say that the two variables are correlated. But knowing that two variables are correlated does not tell us whether one causes the other. We know, for instance, that there is a correlation between the number of roads built in Europe and the number of children born in the United States.
Does that mean that if we want fewer children in the U. Or, does it mean that if we don't have enough roads in Europe, we should encourage U.
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.
Positive and Negative Correlation | eMathZone
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. 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.
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.
Types of Relationships
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.
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.
Not all positive nor negative curves are straight lines, and some curves are parabolic, that is, they take the shape of a U or an inverted U, as is demonstrated in Figure 10, shown below. To the left of point C, called the maxima, slopes are positive, and, to the right of point C, they are negative. You can determine the slope of a parabola by drawing a tangent touches at a single point line to any point on the curve.
You can see below that a point such as R is then selected on the line, and a right angled triangle can be constructed which joins points R and B. We can then calculate the rise over the run between points B and R from the distance of the height and the base of the triangle. So, we can generalize to say that the slopes of a non-linear line are not constant like a straight line and will vary in sign and in value.
You will find that a knowledge of slope calculations enhances your understanding of the dynamics of graphs.
It will likely improve your marks in economics, since many test questions require you to illustrate your thinking with graphs. Summary A person from an Eastern culture once observed, "A picture is worth a thousand words.
Without them, we would be forced to examine thousands, or tens of thousands, of bits of statistical information to determine economic relationships. Many economic researchers over the years have done that work for you, and it gets expressed in nice little packages called graphs. They convey information easily, efficiently, and effectively, and can stimulate good thought and discussion.
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