Mathematicians seem to simply call these scenarios "non-linear" or "curvilinear" relationships, without seeming to notice that there are invariably two distinct relationships being identified by the data. While I have always used the term "split" effect to describe such phenomenon, I have not been able to find this phenomenon acknowledged or identified (by any particular term) amongst economists or mathematicians. Thus, we often see two or more different effects express themselves through a full range of data. This is because at very high rates of taxation, people either lose interest in working, or they start to seek ways of hiding their income from the government. However, after a certain tax rate is reached, we start to see a new effect take place wherein the tax revenue drops off as the tax rate is increased further. I call this phenomenon a "split" effect.įor example, in the Laffer curve, we at first see the government raise more tax revenue as tax rates increase because they collect more money from citizens. If r > 0 then y tends to increase as x is increased. If r < 0 then y tends to decrease as x is increased. The sign of r indicates the direction of the linear relationship between x and y. The value of r lies between 1 and 1, inclusive. However, sometimes one effect drops off and then a new effect takes over. The linear correlation coefficient has the following properties, illustrated in Figure 10.4 'Linear Correlation Coefficient '. In economics, we're always interested in identifying "effects" that take place between variables. The R base function pairs () can be used. This is useful to visualize correlation of small data sets. Here, we’ll describe how to produce a matrix of scatter plots. In Problem #3, illustrations A and B, you show something we see in economics quite a bit. Previously, we described the essentials of R programming and provided quick start guides for importing data into R.
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