Correlation in a statistic is a factor used to describe the relationship between one variable and the other variable. In a graph, there are two axes: X-axis (explanatory variable) and Y-axis (responses variable). For example, If we would use height to predict weight then the height would be the explanatory variable and the weight would be the response variable. Then we would use the data of the height and the weight to calculate for the correlation coefficient (r).
The correlation coefficient(r), rage from -1 to 1. When the r-value equal to -1, it shows that the two variables have a negative relationship/correlation; in this case, it means that as the height increase, the predicted weight will decrease. On the other hand, if the r-value would to equal to 1, the two variables will have a positive relationship/correlation which means that as the height increase the weight will also increase. Yet, if the r-value equal to 0, the two variables don’t have any relationship at all. However, a perfect r-value of -1, 0, or 1 is not a value that we’ll get calculating real datasets because real datasets won’t have such an exact relationship between real datasets.
The equation for r is r =1/n-1∑(xi-x/xs)(yi-y/ys), however, it would take forever to plug in and solve this equation; so we use the Ti3 calculator instead. In our case of using height to predict weight, we receive an r-value of .76. This value shows a high correlation between the two variables, therefore, it’s positive to use the height to predict the weight.
Watch me solving for the r and r-square value!