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7.4
Simple Linear Regression
P
urpose
The role this topic plays in quantitative reasoning
Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data.
You have built up your expertise in the in some of these skills: collection, organization, preliminary
analysis, and some presentation of the data. You have also explored statistical tools for understanding
central tendency and variation. Additionally, you have analyzed the process of performing data analysis.
Now you’re ready to study more advanced patterns contained in data.
Linear regression
is a way to
build a model to determine how strong the relationship is between two variables. One way to use linear
regression is for predictive modeling. The reliability of this predictive tool is based upon the strength of
the relationship between the two variables which is measured by the correlation coefficient.
L
earning Goals
What you should learn while completing this activity
1. Explore the meaning of the correlation coefficient through its calculation, visual representations, and
limitations.
2. Effectively and appropriately use the linear regression equation for prediction
3. Explain the difference between correlation and causation.
D
iscovery
Finding out for yourself
Imagine that you had the results of the first quiz and the first exam for all of the students in a college
mathematics class. Who would you expect to score higher on the first midterm exam, students who
scored 8, 9, or 10 (on a 10 point quiz) or a 6 or 7? For a given score earned on the quiz, what would you
predict that particular student to score to be on the mid-term exam? How could you measure the strength
of the relationship between a student’s score on the quiz and his or her score on the mid-term? How
would you predict a student’s test score if you knew her quiz score? How could you use this information
to advise students in preparing for the test?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. How does you compute the mean and standard deviation of a data set?
2. How do you calculate the z-score (the number of standard deviations above or below the mean)?
3. How do you find the equation of line, given a slope and a point on that line?
4. What do you know about correlation?
5. What does it mean for one event to
cause
another event?