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10.1 Scatter Plots and Trend Lines

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1 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

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

3 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.

4 Correlations

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

6 Plot the data on a graph paper.

7 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?

8 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.

9 Correlation Coefficient (r)
– r close to r close to 1 – r close to r close to 0.5

10 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.

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

12 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 …

13 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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