Math CC7/8 – May 2 Math Notebook: Things Needed Today (TNT): TwMM 4.3

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Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

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Presentation transcript:

Math CC7/8 – May 2 Math Notebook: Things Needed Today (TNT): TwMM 4.3 Pencil/Math Notebook/Book TwMM 4.3 Math Notebook: Topic: Correlation Coefficients & Outliers HW: TwMM 100 #6-8, 19-20, 25

What’s Happening Today? Lesson 4.3 – Correlations Coefficients & Outliers

pg. 87

Question What does a correlation coefficient of 1, 0, or -1 suggest to you about the relationhip between 2 variables?

EVERYONE Add highlighted information to your notes! pg. 87-88 EVERYONE Add highlighted information to your notes!

pg. 88 A correlation of 1 means that there is a perfect linear relationship between two variables with a positive slope.

pg. 88 0.4 -1 0.8 -0.4 -0.8 0.0

Pink Dots – Wood Frame Roller Coaster Blue Dots – Steel Frame Coasters pg. 89 When you inspect a scatter plot, often you are looking for a strong associations between the variables. This scatter plot shows the relationship between the top speed of a roller coaster and its maximum drop.

pg. 89 Yes. These data points are tightly clustered in an upward sloping linear trend, so a linear model would give accurate predictions.

The correlation coefficient is closest to r = 1. pg. 89 The correlation coefficient is closest to r = 1. Notice how all of the clusters are close to the line.

pg. 90

pg. 90 The points are less tightly clustered in an upward sloping trend, so a linear model is going to be less reliable as a predictor of top speed for a given track length.

The correlation coefficient is closest to r = 0.5. pg. 90 The correlation coefficient is closest to r = 0.5. Notice: the data is more spread out

A coaster could have a long track, but height doesn’t change much. pg. 90 No. A coaster could have a long track, but height doesn’t change much. Without large drops, coasters would not achieve high speeds.

pg. 91

pg. 91 The points are less tightly clustered than in question C, so a linear model will not be a reliable predictor of top speed for a given ride time.

The correlation coefficient is closest to r = 0 or…..possibly 0.5 pg. 91 The correlation coefficient is closest to r = 0 or…..possibly 0.5

below Outlier No Outlier No No No

pg. 91 Answers vary… (2800, 120) (1300, 100)

pg. 92

pg. 92 These data points are tightly clustered in a downward sloping linear trend, so a linear model would give accurate predictions of number of riders based on rider age.

The correlation coefficient is closest to pg. 92 2. The correlation coefficient is closest to r = -1 3. Are any of the data points outliers? If so, estimate the coordinates of those points. (14, 45) (16, 60) (17, 70) (72, 2) (77, 2) (80, 1)

pg. 92 Yes, it is possible to have a strong correlation coefficient that indicates a strong relationship even when there are a few outliers.