Question

When looking at attendance data for the 2014-2015 school year, a principal graphed number of tardies. x, a student had when compared to their grade point average y. The principal found the correlation coefficient to be R= -0.94.

There is a strong or weak relationship between the number of tardies and the GPA?
The slope of this graph is positive or negative?

Answer 1

We need to remember that the limits for this correlation coefficient are
`-1 \leq r \leq 1`

So then for the firt question:

Since the |r| =0.94 and is near to 1 we can ensure that we have a strong relationship between the two variables of interest

And for the second question:

The slope for this case would be negative since if one variable increase the other decrease (that represent the negative value for r)

Explanation:

For this case we are comparing the number of tardies. x, a student had when compared to their grade point average y.

We alo know that the correlation coefficient between the two variables using this formula:

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

And for this case
`r =-0.94`

We need to remember that the limits for this correlation coefficient are
`-1 \leq r \leq 1`

So then for the firt question:

Since the |r| =0.94 and is near to 1 we can ensure that we have a strong relationship between the two variables of interest

And for the second question:

The slope for this case would be negative since if one variable increase the other decrease (that represent the negative value for r)