Scatter plot terms

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# Scatter plot terms

A scatter plot is a special type of graph designed to show the relationship between two variables. With regression analysis, you can use a scatter plot to visually inspect the data to see whether X and Y are linearly related.

The following are some examples. This figure shows a scatter plot for two variables that have a nonlinear relationship between them.

Each point on the graph represents a single XY pair. Notice that starting with the most negative values of Xas X increases, Y at first decreases; then as X continues to increase, Y increases. With a linear relationship, the slope never changes. In this example, one of the fundamental assumptions of simple regression analysis is violated, and you need another approach to estimate the relationship between X and Y.

One possibility is to transform the variables; for example, you could run a simple regression between ln X and ln Y.

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This often helps eliminate nonlinearities in the relationship between X and Y. Another possibility is to use a more advanced type of regression analysis, which can incorporate nonlinear relationships. This figure shows a scatter plot for two variables that have a strongly positive linear relationship between them. The correlation between X and Y equals 0. The figure shows a very strong tendency for X and Y to both rise above their means or fall below their means at the same time. The straight line is a trend linedesigned to come as close as possible to all the data points.

The trend line has a positive slope, which shows a positive relationship between X and Y. The points in the graph are tightly clustered about the trend line due to the strength of the relationship between X and Y.

Note: The slope of the line is not 0. The next figure shows a scatter plot for two variables that have a weakly positive linear relationship between them; the correlation between X and Y equals 0. This figure shows a weaker connection between X and Y.

Note that the points on the graph are more scattered about the trend line than in the previous figure, due to the weaker relationship between X and Y. The next figure is a scatter plot for two variables that have a strongly negative linear relationship between them; the correlation between X and Y equals —0. This figure shows a very strong tendency for X and Y to move in opposite directions; for example, they rise above or fall below their means at opposite times.

The trend line has a negative slope, which shows a negative relationship between X and Y. The next figure is a scatter plot for two variables that have a weakly negative linear relationship between them. The correlation between X and Y equals —0. This figure shows a very weak connection between X and Y.

Note that the points on the graph are more scattered about the trend line than in the previous figure due to the weaker relationship between X and Y. Alan AndersonPhD is a teacher of finance, economics, statistics, and math at Fordham and Fairfield universities as well as at Manhattanville and Purchase colleges. Outside of the academic environment he has many years of experience working as an economist, risk manager, and fixed income analyst.

Scatter plot of a nonlinear relationship. Scatter plot of a strongly positive linear relationship. Scatter plot of a weakly positive linear relationship. Scatter plot of a strongly negative linear relationship.A Scatter XY Plot has points that show the relationship between two sets of data.

The data is plotted on the graph as " Cartesian x,y Coordinates ". The local ice cream shop keeps track of how much ice cream they sell versus the noon temperature on that day. Here are their figures for the last 12 days:. It is now easy to see that warmer weather leads to more salesbut the relationship is not perfect.

Try to have the line as close as possible to all pointsand as many points above the line as below. Careful: Extrapolation can give misleading results because we are in "uncharted territory".

We can estimate a straight line equation from two points from the graph above. The values are close to what we got on the graph. But that doesn't mean they are more or less accurate. They are all just estimates. Note: we used linear based on a line interpolation and extrapolation, but there are many other types, for example we could use polynomials to make curvy lines, etc.

When the two sets of data are strongly linked together we say they have a High Correlation. Correlations can be negative, which means there is a correlation but one value goes down as the other value increases. Note: I tried to fit a straight line to the data, but maybe a curve would work better, what do you think? Hide Ads About Ads. In this example, each dot shows one person's weight versus their height. The data is plotted on the graph as " Cartesian x,y Coordinates " Example: The local ice cream shop keeps track of how much ice cream they sell versus the noon temperature on that day.

Line of Best Fit We can also draw a "Line of Best Fit" also called a "Trend Line" on our scatter plot: Try to have the line as close as possible to all pointsand as many points above the line as below. Interpolation and Extrapolation Interpolation is where we find a value inside our set of data points. Don't use extrapolation too far!A scatterplot displays a relationship between two sets of data.

A scatterplot can also be called a scattergram or a scatter diagram. In a scatterplot, a dot represents a single data point. With several data points graphed, a visual distribution of the data can be seen. Depending on how tightly the points cluster together, you may be able to discern a clear trend in the data. The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship.

If the data points make a straight line going from near the origin out to high y -values, the variables are said to have a positive correlation. If the data points start at high y -values on the y -axis and progress down to low values, the variables have a negative correlation. As number of candy bars increase, the amount of total cost increases. A situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam vs.

This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general, the rule will hold true that as the amount of time studying increases so does the grade received.

Notice that the data points are spread out even more in these graphs. The closer the data points lie together to make a line, the higher the correlation. In these graphs, there is still a trend in the data, so we would say that the data has a weak or lower correlation. The data points are spread out even more in this graph. This means t here is no trend to the data; t hus, there is no correlation.

This graph illustrates how a person's weight might change depending on how much they run in a week. It records the change in weight for a group of people, all of whom started out weighing 90kg. Each person runs a different number of kilometers each week for an unspecified period of time. You can conclude from the graph that as the number of kilometers run each week increases, a person's weight decreases. When points are graphed on a scatterplot, it is possible to find a line of best fit—a straight line that best represents the data on a scatterplot.

Here's the same graph with the line of best fit drawn in.Scatter plots are important in statistics because they can show the extent of correlation, if any, between the values of observed quantities or phenomena called variables.

If no correlation exists between the variables, the points appear randomly scattered on the coordinate plane. If a large correlation exists, the points concentrate near a straight line. Scatter plots are useful data visualization tools for illustrating a trend. Correlation is often confused with causation, either accidentally as a result of false or unproved hypotheses or deliberately with intent to deceive. However, in the pure sense, while a scatter plot can reveal the nature and extent of correlation, it says nothing about causation.

This video from RodCastMath explains more about negative and positive correlation on a scatter plot. See also: graph theorypictographbar graphpoint-to-point graphsparklinetime series chart. Please check the box if you want to proceed. Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business. Risk management is the process of identifying, assessing and controlling threats to an organization's capital and earnings.

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Besides showing the extent of correlation, a scatter plot shows the sense of the correlation: If the vertical or y -axis variable increases as the horizontal or x -axis variable increases, the correlation is positive.

### Interpreting Scatterplots

If the y -axis variable decreases as the x -axis variable increases or vice-versa, the correlation is negative. If it is impossible to establish either of the above criteria, then the correlation is zero.

See also: graph theorypictographbar graphpoint-to-point graphsparklinetime series chart This was last updated in December Powered by WordPress. Scatter plots are frequently used in data science and machine learning projects. Both solutions will be equally useful and quick:. You can also find the whole code base for this article in Jupyter Notebook format here: Scatter plot in Python. You can download it from: here.

Scatter plots are used to visualize the relationship between two or sometimes three variables in a data set. The idea is simple:.

Following this concept, you display each and every datapoint in your dataset. This is a scatter plot. At least, the easiest and most common example of it. This particular scatter plot shows the relationship between the height and weight of people from a random sample. As we discussed in my linear regression articleyou can even fit a trend line a. This above is called a positive correlation. The greater is the height value, the greater is the expected weight value, too.

Of course, this is a generalization of the data set. There are always exceptions and outliers! Note: By the way, I prefer the matplotlib solution because I find it a bit more transparent. The first two lines will import pandas and numpy.

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The third line will import the pyplot from matplotlib — also, we will refer to it as plt. Well, in real data science projects, getting the data would be a bit harder. You should read. This is a random generator, by the way, that generates height and weight values — in numpy array format. By using the np. Again, preparing, cleaning and formatting the data is a painful and time consuming process in real-life data science projects.

But in this tutorial, we are lucky, everything is prepared — the data is clean — so you can push your height and weight data sets directly into a pandas dataframe called gym by running this one line of code:.

Okay, all set, we have the gym dataframe. It starts with: gym. The x and y values — by definition — have to come from the gym dataframe, so you have to refer to the column names: 'weight' and 'height'! A quick comment: Watch out for all the apostrophes! I know from my live workshops that the syntax might seem tricky at first.

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In this one, we will use the matplotlib library instead of pandas. In my opinion, this solution is a bit more elegant. But from a technical standpoint — and for results — both solutions are equally great.

Again: this is slightly different and in my opinion slightly nicer syntax than with pandas. But the result is exactly the same.Definition: The Scatter Diagram Method is the simplest method to study the correlation between two variables wherein the values for each pair of a variable is plotted on a graph in the form of dots thereby obtaining as many points as the number of observations. Then by looking at the scatter of several points, the degree of correlation is ascertained.

The degree to which the variables are related to each other depends on the manner in which the points are scattered over the chart. The more the points plotted are scattered over the chart, the lesser is the degree of correlation between the variables. The more the points plotted are closer to the line, the higher is the degree of correlation.

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The following types of scatter diagrams tell about the degree of correlation between variable X and variable Y. Thus, the scatter diagram method is the simplest device to study the degree of relationship between the variables by plotting the dots for each pair of variable values given.

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Business Jargons A Business Encyclopedia. Accounting Banking Business Business Statistics. Thank you so much for this clear and short information. This is short and understandable.

It is an X-Y diagram that shows a relationship between two variables. It is used to plot data points on a vertical and a horizontal axis. The purpose is to show how much one variable affects another. The scatter plot shows that there is a relationship between monthly e-commerce sales Y and online advertising costs X. This line is used to help us make predictions that are based on past data.

Usually, when there is a relationship between 2 variables, the first one is called independent. The second variable is called dependent because its values depend on the first variable. Types of Correlation in a Scatter Plot. In the above text, we many times mentioned the relationship between 2 variables.

Thi is called correlation. When one variable dependent variable increase as the other variable independent variable increases, there is a positive correlation. Height and clothes size is a good example here. When the height of a child increase, the clothes size also increase. As you might guess, we have negative correlation when the increase of one variable leads to decrease in the other. Car age and car price are correlating negatively. Usually, when car age increase, the car price decrease.

As you see in the negative correlation, the trend line goes from a high-value on the y-axis down to a high-value on the x-axis. No correlation means there is no relationship between the variables. The above graphs are made by www.

## scatter plot

They show you large quantities of data and present a correlation between variables. Advantages of Scatter plots:. Disadvantages of Scatter Plots:. It is true that Scatter plots have some limitations. However, when used correctly, they are a great tool for overviews and showing patterns and relationship between some datasets.

If you need some real-life examples of how Scatter charts work, check our post simple linear regression examples. Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI Artificial IntelligenceIoT Internet of Thingsprocess automation, etc. 