# AP Statistics 2.4 Exploring Data

AP Statistics: Exploring Data Drill 2, Problem 4. This coefficient shows a relationship of...what?

AP Statistics | Exploring Data |

Exploring Data | Exploring Bivariate Data |

Language | English Language |

### Transcript

showing "hours spent watching Hulu after dinner" on the x-axis and "hours of homework completed

after dinner" on the y-axis. We calculated a linear correlation coefficient

of r = -0.27. This coefficient shows a relationship of... what?

And here are the potential answers...

All we have to do is interpret the r-value to figure out whether or not the hypothesis is true.

Remember that r is the correlation coefficient of a set of data.

In other words, it tells us how good of an approximation we have.

In this case, we have a linear approximation, so r tells us how close to a line the data forms.

R values range between -1 and 1. The closer

r is to 0, the worse our approximation. However, as r approaches either end of its range, the

better the approximation. How can the correlation get better by moving

in either direction? Well, the more negative r is, the better a

negative correlation we have. The more positive, the better the positive correlation.

But what does THAT mean?

A positive correlation means that the data has a positive linear

slope, and a negative correlation means it has a negative linear slope.

We have an r value of -.27, which means there is a negative correlation.

Just from this knowledge, we can eliminate (A), (B), and (E).

-.27 is closer to 0 than -1. In other words, it's closer to having no correlation

than having a perfect correlation. Which means that the correlation is pretty weak.

Since we have a weak negative correlation,

our answer is (C). Even though the correlation is weak, there

is definitely a negative correlation... ...which means that the more Hulu you watch,

the less homework you'll get done.