Transcript 2-2 LINEAR REGRESSION OBJECTIVES Be able to fit a regression line to a scatterplot. Find and interpret correlation coefficients. Make predictions based on lines of best fit. Slide 1 Financial.

2-2
LINEAR REGRESSION
OBJECTIVES
Be able to fit a regression line to a
scatterplot.
Find and interpret correlation
coefficients.
Make predictions based on lines of
best fit.
Slide 1
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.
Key Terms
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Slide 2
line of best fit
linear regression line
least squares line
domain
range
interpolation
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extrapolation
correlation coefficient
strong correlation
weak correlation
moderate correlation
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.
Example 1
Find the equation of the linear regression line for
Rachael’s scatterplot in Example 1 from Lesson 2-1.
Round the slope and y-intercept to the nearest
hundredth. The points are given below.
(65, 102), (71, 133), (79, 144), (80, 161), (86, 191),
(86, 207), (91, 235), (95, 237), (100, 243)
Slide 3
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.
Example 2
Interpret the slope as a rate for Rachael’s linear
regression line. Use the equation from Example 1.
Slide 4
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.
CHECK YOUR UNDERSTANDING
Approximately how many more water bottles will
Rachael sell if the temperature increases 2 degrees?
Slide 5
Financial Algebra
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EXAMPLE 3
How many water bottles should Rachael pack if the
temperature forecasted were 83 degrees? Is this an
example of interpolation or extrapolation? Round to the
nearest integer.
Slide 6
Financial Algebra
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EXAMPLE 4
Find the correlation coefficient to the nearest hundredth
for the linear regression for Rachael’s data. Interpret
the correlation coefficient.
Slide 7
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.
CHECK YOUR UNDERSTANDING
Find the equation of the linear regression line of the
scatterplot defined by these points: (1, 56), (2, 45),
(4, 20), (3, 30), and (5, 9). Round the slope and
y-intercept to the nearest hundredth.
Find the correlation coefficient to the nearest
thousandth. Interpret the correlation coefficient.
Slide 8
Financial Algebra
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EXTEND YOUR UNDERSTANDING
Carlos entered data into his calculator and found a
correlation coefficient of -0.28. Interpret this
correlation coefficient.
Slide 9
Financial Algebra
© 2011 Cengage Learning. All Rights Reserved.