Pre-Calculus
Unit 3 WS 3-1: Linear Regression
Pd:
Name:
1. The manager of a telemarketing company recorded figures for the number of hours (h) each employee
worked per day and the number of sales (s) that employee made. The (h,s) data for several employees
over several days were:
(8,17) (4,8) (5,12) (7,14) (8,15) (7,16) (5,10) (7,13) (3,7) (8,14)
a.) What is the independent variable?
v\&lA>(t~>
Dependent variable?
b.) find the equation for the line of best fit with your calculator.
c.) What is the value of V?
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» * ? ^ : What does that mean?
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d.) Use your equation to predict the number of sales that an employee could produce in 6 hours.
2. The data in the table below represents the height of water in a jar versus the # of marbles
placed in the jar. Make a scatter plot of the data. Be sure to label the axes.
Number of
marbles in
jars
Height of
Water in jar
(in.)
5
10
15
20
25
6
7.25
8
9.25
9.375
a. What is the independent variable?
. Dependent variable?
b. Find the linear regression equation with a calculator.
c. What is the value of "r"?
«4l ? : What does it tell you?
U -
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d. Predict the height of the water if there are 47 marbles in the jar.
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e. Predict the number of marbles needed to raise the water 23.4 inches.
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3. Healthy Lifestyle: The table below shows the age and systolic blood pressure for a group of people
who recently donated blood.
Age
Blood
Pressure
35
128
48
140
24
108
50
135
a. Which is the independent variable?
b.
34
119
55
146
30
132
26
104
41
132
37
121
; Dependent variable ?
Write a prediction equation that relates a person's age to their approximate systolic blood pressure.
y -=•
c. Find the approximate systolic blood pressure of a person 54 years old.
4. The table below shows the annual gross ticket sales 5 (in millions of dollars) for New York Cit's
Broadway shows from 1995 to 2004..
Annual sales (millions)
Year
406
1995
436 499
1996 1997
558
1998
588
1999
603 666 643 721
771
2000 2001 2002 2003 2004
a. Enter the data, where t(time) = 0 for 1995, 1 for 1996, etc..., then find the prediction equation
y b. What is the correlation coefficient?
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c. What does the coefficient say about the data?
d. What will sales be in 2005?
e. What will sales be in 2008?
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