Question
Explain scatter diagram method.
✓
Answer
This method is used to know the nature of correlation between two variables.
- By taking values of variable $X$ on x-axis and corresponding values of $Y$ on $y-$axis with appropriate scale and plotting n sample points $(x_1, y_1), (x_2, y_2)....... (x_n, y_n)$ on the graph paper, a diagram is obtained which is called scatter diagram.
- From the pattern of points on the scatter diagram, nature of correlation and strength of correlation can be known to some extent.
- The following are the types of correlation according to the scatter diagram method.
- $(1)$ Perfect Positive Correlation :
- If all the points of the scatter diagram obtained by plotting $n$ ordered pairs of observations of two correlated variables $x$ and $y,$ lie on one line which goes in upward direction from left to right, then we can say that there is perfect positive correlation between variable $x$ and $y.$
- Where value of $r$ is $+1$.
- When the changes in the values of both the variables are in the same direction and in the same proportion we get the following scatter diagram.
- $(2)$ Perfect Negative Correlation :
- If all the points of the scatter diagram obtained by plotting $n$ ordered pairs of observations of two correlated variables $x$ and $y,$ lie on one line which goes in downward direction from left to right ,then we can say that there is perfect negative correlation between variable $x$ and where value $r$ is $-1.$
- When the changes in the values of both the variables are in the opposite direction and in the same proportion we get the following scatter diagram.
- $(3)$ Partial positive correlation :
- If all the point of scatter diagram are not on one line but lie around line which is going in upward direction from left to right then we say there is partial positive correlation between $x$ and $y$ where value of $r$ lies between $0$ and $1.$
- When the changes in the values of both the variables are in the same direction but not in the same proportion we get the following scatter diagram.
- $(4)$ Partial negative correlation :
- If all the point of scatter diagram are not on one line but lie around line which is going in downward direction from left to right then we say there is partial positive correlation between $x$ and $y$ where value of r lies between $-1$ and $0.$
- When the changes in the values of both the variables are in the opposite direction but not in the same proportion we get the following scatter diagram.
- $(5)$ Lack of correlation :
- If all the points of scatter diagram are not in particular direction but lie randomly without forming any specific pattern then we can say that there is lack of correlation.
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