AP Statistics 2.4 Exploring Data
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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.