Linear Models and Scatter Plots 2015. Objectives Interpret correlation Use a graphing calculator to...
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Transcript of Linear Models and Scatter Plots 2015. Objectives Interpret correlation Use a graphing calculator to...
Linear Models and Scatter Plots
2015
Objectives
• Interpret correlation
• Use a graphing calculator to find linear models and make predictions about data.
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HWQ 8/11/15
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3 13 2, find f x x f x
Extra practice:
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13 3 10, find f x x f x
Interesting result:
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2
1
16 , 0 4
find
f x x x
f x
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x2 4
–2
– 4
y
2
4
6
A scatter plot represents data graphically using points plotted on a rectangular coordinate system.
Example: (x, y)
(1, – 4)
(2, – 2)
(3, – 1)
(4, 0)
(5, 2)
(6, 4)
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In a collection of ordered pairs (x, y), if y tends to increase as x increases, the collection has a positive correlation.
x
y
x
y
x
y
If y tends to decrease as x increases, the collection has a negative correlation.
positive correlation no correlationnegative correlation
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Example: The average salary S (in millions of dollars) for professional baseball players from 1996 through 2002 is shown in the table. Let t = 6 represent the year 1996. Draw the scatter plot.
Year Salary, S1996 1.11997 1.31998 1.41999 1.62000 1.82001 2.12002 2.3
S
4t
8
1
2
Year (6 1996)
Sal
ary
(in
mil
lion
s of
dol
lars
)
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Year Salary, S1996 1.11997 1.31998 1.41999 1.62000 1.82001 2.12002 2.3
Graphing Utility: Draw the scatter plot that describes the data.
Stat Plot Menu:
Zoom Menu:
Stat Edit Menu:
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Finding a linear model to represent the relationship described by a scatter pot is called fitting the line to data.
Year Salary, S1996 1.11997 1.31998 1.41999 1.62000 1.82001 2.12002 2.3
4 t8
S
1
2
Example: The table and scatter plot for the average salary S (in millions of dollars) for professional baseball players from 1996 through 2002 is shown. Let t = 6 represent the year 1996.
Find the equation of the line.
Example continues.
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Year Salary, S1996 1.11997 1.31998 1.41999 1.62000 1.82001 2.12002 2.3
4 t8
S
1
2
(6, 1.1)
(12, 2.3)
The equation of this line is S = 0.2t – 0.1.
This line approximates the data.
Example continued:
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Year Salary, S1996 1.11997 1.31998 1.41999 1.62000 1.82001 2.12002 2.3
Graphing Utility: Find a linear model that describes the data.
Stat Menu:
A linear model for this data is S = 0.2t – 0.14. This equation is very close to the equation found using two data points. What does the model predict Baseball players salaries to be in 2015?
Stat Edit:
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The correlation coefficient (or r-value) of the data gives the measure of how well the model fits the data.
The closer |r| is to 1, the better the points can be described by a line.
r = 0.99 strong positive
correlation
r = – 0.93 negative
correlation
0 13
2
0
52.6
52.30 13
r = 0.66 weak correlation
509050
100
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Year Radio
Stations, R1970 6,7601975 7,7441980 8,5661985 10,3591990 10,788
1995 11,8342000 13,058
A linear model for this data is R = 209.257t +6733.857.
15,104
You Try: The number R of U.S. radio stations for selected years is shown in the table. Use a graphing utility to find a linear model that describes the data. Let t=0 correspond to 1970.For the year 2010, how many radio stations does the model predict?
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Homework
Pg. 773-6 all, 7-15 odds, 27-37 odds