Question

A high positive correlation is found between college students' age and their GPA. However, if one student aged 44 with a high GPA is omitted from the study, the correlation all but disappears. This is an example of:

Answer 1

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.

Explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

By definition an outlier is a point "that diverges from an overall pattern in a sample". The residual for this outiler is usually high and when we have presence of outliers our model probably would be not significant since the tendency is not satisfied.

By definition and influential point is a point that has "a large effect on the slope of a regression line fitting the data:. And usually represent values that are too high or low respect to the others.

Solution to the problem

For this case we assume that we have a high positive correlation between college student's age and the GPA.

So we assume that
`0.7 \leq r \leq 1`

And We see that after introduce the value of 44 for the age the correlation disappears, that means decrease significantly.

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.