10.1 Scatter Plots and Trend Lines CCSS: S-ID 6. 6. 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

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

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.

Correlations

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

Plot the data on a graph paper.

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?

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.

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

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.

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

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 …

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