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**10.1 Scatter Plots and Trend Lines**

CCSS: S-ID Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models

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Essential Question: How can you describe the relationship between two variables and use it to make predictions?

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**Describing How Variables Are Related in Scatter Plots**

Two-variable data is a collection of paired variable values scatter plot: a graph of points with one variable plotted along each axis. Correlation is a measure of the strength and direction of the relationship between two variables.

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Correlations

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**Explore: The table present two-variable data for 7 cities**

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**Plot the data on a graph paper.**

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**Reflections What are the two variables? Are the variables correlated?**

Why are the points in a scatter plot not connected in the same way plots of linear equations are?

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**Answers 1. The 2 variables are Latitude and Temperature**

2. The variables are negatively correlated. 3. A straight line indicates a continuous set of points. Data in scatter plot are represented by discrete points. Line segments between points would incorrectly imply either data or function along segments between the scattered points.

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**Correlation Coefficient (r)**

– r close to r close to 1 – r close to r close to 0.5

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**Example 1: Use a scatter plot to estimate the value of r**

Example 1: Use a scatter plot to estimate the value of r. lndicate whether r is closer to - 1, - 0.5, 0, 0.5, or l.

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Answer This is strongly correlated and has a negative slope, so r is close to -1.

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Ex. 2: This data represents the football scores from one week with winning score plotted versus losing score. The correlation coefficient r is close to …

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Assignment Use a scatter plot to estimate the value of r. lndicate whether r is closer to - 1, - 0.5, 0, 0.5, or l

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