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© 2014 Pacific Crest
349
H
ardest Problem
How hard
can
it be? Can you still use what you’ve learned?
Based on the Models, the Methodologies, and the Demonstrate Your Understanding (DYU) problems in
this activity, create the
hardest
problem you can. Start with the hardest DYU problem in this experience
and by contrasting and comparing it with the other DYU problems, play “What if” with the different
conditions and parameters in the various problems.
Can you still solve the problem? If so, solve it. If not, explain why not.
What are the conditions and parameters that make a problem where you must determine the linear regression
equation (for a set of data with two variables) a difficult problem to solve?
T
roubleshooting
Find the error and correct it!
Content available online at companion website.
Identify six different common errors. For each, provide a suggestion for preventing or avoiding that
error in the future.
M
aking it Matter
Solving problems in your life
●
Create a linear regression model of your past courses taken along with your current courses. Estimate
the number of hours invested in each course and determine what your grade was or most likely be on
a scale of 0 to 4. See if there is a correlation and if the correlation is strong enough to predict future
grades based upon hours you studied for a particular course.
●
Create a small study of how happy your friends are based upon how many close friends they have.
Identify 15 friends and ask them two questions: “On a scale of 0 to 10, how happy are you?” and
“How many close friends do you have?” See if there is a positive correlation and if so how many
friends you need to have in order to be happy.
●
Perform a study of teachers and learning. Ask your friends about their courses: 1) Rate five courses
on a scale of 1 to 10 to represent how much you learned and 2) For these same courses, how effective
was your instructor on a scale of 1 to 10. Collect data from seven different students and perform
a linear regression model to predict how much learning is possible based upon the quality of the
teacher.
L
earning to Learn Mathematics
Reflecting on and appreciating your learning
1. How does wanting something to be true influence your thinking when you’re creating models? Why/
how?
2. What determines the limitations when it comes to creating and applying mathematical models?
3. Why is variation so important in statistics?
7.4 Simple Linear Regression