11.1
Correlation
In statistics, if the values of one variable move in relationship with the values of the other variable, then the two variables are said to have a correlation.
Consider the scatter plot of ice cream sales as a function of the temperature, which shows a distinct linear pattern.
Since ice cream sales increase with temperature, these variables have a positive correlation.
Now, consider the scatter plot of hot chocolate sales as a function of temperature. The data points in this case also have a linear pattern and hence have a correlation.
But, hot chocolate sales decrease with the rise in temperature, so the variables have a negative correlation.
Apart from linear, other patterns can also be observed in real life. For example, as time passes, there is an exponential rise in the COVID cases before reaching a plateau. So this is a non-linear, positive correlation.
There can be cases where there is no correlation between the two variables. For example, the number of movies watched has no correlation with shoe size.
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
- Variable a increases as variable b increases
- Variable a decreases as variable b decreases
In a negative correlation, one variable, a, decreases as the other variable, b, increases and vice versa. For example, altitude and temperature are negatively correlated since temperature decreases with the increase in altitude.
Further, when two variables exhibit no relationship, there is said to be zero correlation between them. For example, there is no relation between the number of songs listened to by individuals and their height.
Additionally, correlation can be linear or non-linear. A linear relationship is one where a straight line shows the correlation between two variables. An exponential relationship is an example of a non-linear correlation.
In statistics, if the values of one variable move in relationship with the values of the other variable, then the two variables are said to have a correlation.
Consider the scatter plot of ice cream sales as a function of the temperature, which shows a distinct linear pattern.
Since ice cream sales increase with temperature, these variables have a positive correlation.
Now, consider the scatter plot of hot chocolate sales as a function of temperature. The data points in this case also have a linear pattern and hence have a correlation.
But, hot chocolate sales decrease with the rise in temperature, so the variables have a negative correlation.
Apart from linear, other patterns can also be observed in real life. For example, as time passes, there is an exponential rise in the COVID cases before reaching a plateau. So this is a non-linear, positive correlation.
There can be cases where there is no correlation between the two variables. For example, the number of movies watched has no correlation with shoe size.
From Chapter 11:
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11.1 : Correlation
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11.2 : Coefficient of Correlation
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11.3 : Calculating and Interpreting the Linear Correlation Coefficient
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11.4 : Regression Analysis
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11.5 : Outliers and Influential Points
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11.6 : Residuals and Least-Squares Property
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11.7 : Residual Plots
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11.8 : Variation
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11.9 : Prediction Intervals
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11.10 : Multiple Regression
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