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What you will learn today1. New vocabulary2. How to determine if data points are related3. How to develop a linear regression equation4. How to graph a linear inequality
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Correlation and Best-Fitting LinesVocabulary:
Scatter Plot is a graph used to determine whether there is a relationship between paired data (e.g. exercise and heart rate). It looks like a bunch of dots on a graph.
Positive correlation: No Correlation
Negative correlation:
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Determining Types of Correlation Provided by Mrs. C.
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Steps for Developing a “Best Fit Line”
Step 1: Draw a scatter plot of the data (an accurate plot)
Step 2: Sketch the line that appears to follow most closely the pattern of the points. There should be as many points above the line as below it.
Step 3: Choose two points on the line and estimate the coordinates of each point. These points do not have to be from the original data set.
Step 4: Find the equation of the line by finding the slope and using one of the linear equation forms.
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Example The data pairs give the average speed of
an airplane during the first 10 minutes of flight, with x in minutes and y in miles per hour. Approximate the best fit line for the data.
(1, 180), (2, 250), (3, 290), (4, 310), (5, 400), (6, 420), (7, 410), (8, 490), (9, 520), (10, 510)
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Homework for Section 2.5 Page 103, 8-10 all, 19, 20, 24, 25
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Graphing Linear Inequalities
How many solutions are there to the equation y < 2?
We have to have a way to note this on a coordinate plane.
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Graphing Linear InequalitiesA linear inequality in two variables is an inequality that can be written in one of the following forms:
Ax + By < C Ax + By < C
These inequalities have many solutions.
CByAx CByAx
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Example Check whether the given ordered pair is
a solution of 2x + 3y > 5.A) (0, 1) B) (4, -1) C) (2, 1)
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Graphing a y <,> mx + b Inequality
Steps:1. Graph the boundary line just as you
would in a y = mx + b equation.2. Decide which side of the boundary line
to shade by testing a point on either side of the boundary line.
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Example Graph y < -2 and 1x
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Another Example Graph y < 2x and 1052 yx
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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You Try Graph 2x + 3y < 6
x-10 -5 5 10
y
-10
-5
5
10
Objective: 2.5 Correlation and Best Fitting Lines, 2-6 Linear Inequalities
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Homework
Page 111, 14, 16, 30, 31, 48, 49