Scatter Plots

In statistics, a Scatter plot or a Scatter diagram is a graph plotted for two variables, taking one variable along the horizontal axis i.e. X-axis & the other variable along the vertical axis i.e. the Y-axis. Generally, the independent variable is taken along the X-axis & the dependent variable is taken along they axis. It helps us to find whether the two variables, say x & y are correlated or not.

If two variables are correlated, then let’s see how they are related.

1. If the pattern of the plotted points moves from bottom to top as we move from left to right on the X-axis, then it means the value of y increases as the value of x increases. Hence, there exists a positive correlation among the variables x & y and the graph is seen to be rising above

2. If the pattern of the plotted points moves from top to bottom to top as we move from left to right on the X axis, then it means the value of y decreases as the value of x increases. Hence, there exists a negative correlation among the variables x & y and the graph is seen to be falling down.

3. If the values of y do not change, as we move from left to right on the X axis, then it means the value of y is constant as the value of x increases. Hence, there exists a correlation among the variables x & y is constant
4. If the pattern of the plotted points does not show a recognizable pattern e. shows a random behaviour as we move from left to right on the X axis, then the two variables are uncorrelated.

Now, we consider some examples.

Example 1: Draw a scatter plot for the following set of values of x & y and identify if they are correlated. If yes, specify the type of correlation present.

The scatter plot clearly shows that graph rises down as the values of x are increased i.e. as we move from left to right on the x axis. Hence the variables x & y are positively correlated.

Since all the points can be joined by a line, hence the correlation is a perfect positive correlation.

Example 2: A company keeps a record of the number of electric units consumed in seven days of a week with respect to the average day temperature.

Construct a scatter plot for the same and check if there exists a relation between the average day temperature & the number of electric units consumed on that day.

The scatter plot clearly shows that graph rises above as the values of x are increased i.e. as we move from left to right on the x axis. Hence the variables x & y are positively correlated.

Since all the points can’t be joined exactly by a line, hence the correlation is a high positive correlation. So, the number of electric units consumed is having a high positive correlation with the average day temperature.

Example 3: Draw a scatter plot for the following set of values of x & y and identify if they are correlated. If yes, specify the type of correlation present.

 The scatter plot clearly shows that graph rises down as the values of x are increased i.e. as we move from left to right on the x axis. Hence the variables

x & y are negatively correlated. Since all the points can’t be joined exactly by a line, hence the correlation is a high negative correlation.

From the above example, we see that the scatter plot is a graph plotted between the two variables which give us information, about the correlation between the two variables involved.

Check Point

Construct the scatter plots for the following given set of values & identify the type of correlation (if it exists) .

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