CK-12-Pre-Calculus Concepts

15.7. Linear Correlation http://www.ck12.org

yˆ= 280. 4167
This number seems remarkably low considering the data. This point is very close to thexintercept, which can be
found using algebra:
0 =− 2660. 4167 + 2940. 9333 x
0. 9046 =x
The interpretation of the point (0.9046, 0) from the model is that when a person has a shoe size of just under 1.0,
then their predicted vocabulary is zero. Shoe sizes below 0.9046 will have a negative vocabulary. Is this reasonable?
It certainly does not make sense that someone could have a negative number of words in their vocabulary. Newborn
babies are born without knowing any words and this number stays flat at 0 for some length of time. Therefore, this
model is not accurate for very low shoe sizes.

3. Shaquille’s shoe size is significantly beyond the scope of the data that the model is based on. The data relates to
   elementary school students and a size 23 shoe is beyond the relevant domain. This means it wouldn’t make sense
   to use this model to predict Shaquille’s shoe size. Shoe size does not cause vocabulary, but the two variables are
   strongly correlated because over time both tend to grow.

Practice

For each correlation coefficient, describe what it means for data to have that correlation coefficient and sketch a
scatterplot with that correlation coefficient.
1.r= 1
2.r=− 0. 5
3.r=− 1
4.r= 0
5.r= 0. 8
The data below shows the SAT math score and GPA for 7 different students.

TABLE15.14:

SAT math

score

595 520 715 405 680 490 565

GPA 3.4 3.2 3.9 2.3 3.9 2.5 3.5

6. Use your calculator to perform a linear regression that models the data. What is the regression equation? What is
   the correlation coefficient?


7. Use the equation from #6 to predict the GPA for a student with an SAT score of 500. Does this prediction seem
   reasonable given the data? Why or why not?


8. What is the relevant domain of this data?


9. Does a high SAT math score cause a high GPA?
   The data below shows scores from two different quizzes for 10 different students.

TABLE15.15:

Quiz 1

Score

15 12 10 14 10 8 6 15 16 13

Quiz 2

Score

20 15 12 18 10 13 12 10 18 15