AP Statistics ­ Aim #14.notebook
Unit 1 - Chapter 3
Least Squares Regression
Aim #14 - How do we determine the line of best fit?
Buzz Words:
least squares regression - a method for finding a line that
summarizes the relationship between two variables
Line Regression
A straight line that describes how a response variable (y) changes
as the explanatory variable (x) changes
It is used to predict the value of y for a given value of x!
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AP Statistics ­ Aim #14.notebook
To run a regression, we need to know which variable is explanatory
(independent) and which variable is the response (dependent).
We want a regression line that makes the vertical distances of
the points in a scatterplot from the line as small as possible.
Use least squares regression line (LSRL)
Equation:
∧
y = a + bx
OR
∧
y = ax + b
"y hat" means predicted y-value
"y" means observed y-value
More Buzz Words:
Slope - the amount of change in y when x increases by 1
y-intercept - the value of y when x equals 0
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AP Statistics ­ Aim #14.notebook
eg. Suppose we have explanatory and response variables and we
know that x = 17.222, y = 161.111, sx = 19.696 and sy = 33.479, and
the correlation r = 0.997.
Find the slope and intercept to construct the least-squares
regression line.
y = 131.920 + 1.695x
LSRL on a calculator
1. STAT #4: Clear L1 and L2
2. STAT #1: put data in L1 and L2
L1 is explanatory variable, L2 is responsive variable
3. STAT - CALC #8: run linear regression
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AP Statistics ­ Aim #14.notebook
Wrap it Up!
Manatees are large, gentle sea creatures that live along the Florida
coast. Many manatees are killed or injured by powerboats. Here
are data on powerboat registrations (in thousands) and the number
of manatees killed by boats in Florida in the years 1977 to 1990:
Year
Powerboat
registrations
Manatees killed
1977
447
13
1978
460
21
1979
481
24
1980
498
16
1981
513
24
1982
512
20
1983
526
15
1984
559
34
1985
585
33
1986
614
33
1987
645
39
1988
675
43
1989
711
50
1990
719
47
a) Use your calculator to make a scatterpot of the data.
b) Find the equation of the LSRL and overlay that line on your
scatterplot.
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AP Statistics ­ Aim #14.notebook
c) Predict the number of manatees that will be killed by boats
in a year when 716,000 powerboats are registered.
d) Here are four more years of manatee data:
1991
716
53
1992
716
38
1993
716
35
1994
735
49
Add these points to your scatterplot. Florida took stronger
measures to protect manatees during these years. Do you see
any evidence that these measures succeeded?
Assignment #14 - Worksheet #14
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Attachments
Alg II & Trig ­ HW #1.docx