what does it mean to say that two negativtely are correlated
When two variables are said to be negatively correlated, it means that as one variable increases, the other variable tends to decrease, and vice versa. In other words, there is an inverse relationship between the two variables.
To determine if two variables have a negative correlation, you can use statistical techniques such as calculating the correlation coefficient. The correlation coefficient, also known as Pearson's correlation coefficient (r), measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1.
To calculate the correlation coefficient, you need a set of paired data for the two variables. Here are the steps:
1. Gather the paired data: Collect a set of data points for both variables of interest. For example, if you want to study the correlation between the amount of rainfall and crop yield, you would collect data for different regions or time periods where both variables are measured simultaneously.
2. Calculate the means: Find the mean (average) of each variable from the data set.
3. Calculate the covariance: Subtract the mean of each variable from their respective data points and multiply them together to get a set of products. Take the average of these products to find the covariance.
4. Calculate the standard deviations: Calculate the standard deviation for each variable using their respective data sets.
5. Calculate the correlation coefficient: Divide the covariance by the product of the standard deviations to obtain the correlation coefficient.
If the correlation coefficient is negative (r < 0), it indicates a negative correlation between the two variables. The closer the value is to -1, the stronger the negative correlation. If the correlation coefficient is close to 0, it suggests no or weak correlation.
It is important to note that correlation does not imply causation. A negative correlation between two variables does not necessarily mean that one causes the other to decrease. It simply means that they tend to move in opposite directions.