Let's start by reviewing what a correlation is. Then, we will talk about positive and negative correlations.
Correlated Variables and Correlation Types
We say that two variables are correlated when a change in one is associated with a change in the other. If we plot the data points for two correlated variables, we will see that they fall along a line. We can model the data set using a trend line.
If the slope of the trend line is positive, we say that we have a positive correlation. A negative trend line slope indicates a negative correlation.
Relation of a Positive Correlation with Direct Variation
We can write the relation for two variables that vary directly as shown below.
y/x= k → y = kx
In this equation, y and x represent the variables directly related and we call k the constant of variation. We can compare this equation to the slope-intercept form, where m represents the slope of the line and b the y-intercept.
y= mx+b
By direct comparison, we can see that for variables directly related, the constant of variation is the slope of the relation's line. Therefore, if we were modeling a data set using a direct variation as the trend line, a positive constant of variation would imply a positive correlation.
