Math 1 · Unit 10 · Lesson 3 · part 4 of 5
The surprise: a big r, and still the wrong family
Here is the surprise.
The surprise: a big r, and still the wrong family
Here is the surprise. Some gnats are counted every hour: 12, 20, 35, 60, 80 after 0, 1, 2, 3, 4 hours. Fit a line.
r is about 0.98. But the residuals are +5.8, −3.8, −6.4, +1.0, +3.4: plus, minus, minus, plus, plus. The points start above the line, dip below it, and come back above. That is a curved pattern, a U. The data is bending upward, and a line is the wrong family, even with r so close to 1.
A big r does not mean a line is right.r only measures how close the points are to a line. A gentle curve can be close to a line and still not be one. That is why you never use r alone. Use all three together: the scatter plot (what shape do you see?), r (how tight is it to a line?), and the residual plot (is there a pattern left over?). Lesson 4 fits the gnats with the family they really belong to.