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Algebra 2

Algebra 2. 2.5 Correlation and Best Fitting Lines. Learning Targets. Students should be able to… Use a scatter plot to identify the correlation shown by a set of data. Approximate the best-fitting line for a set of data. EQ:  How can you graph, write, and evaluate linear functions?

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Algebra 2

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  1. Algebra 2 2.5 Correlation and Best Fitting Lines

  2. Learning Targets • Students should be able to… • Use a scatter plot to identify the correlation shown by a set of data. • Approximate the best-fitting line for a set of data. • EQ: How can you graph, write, and evaluate linear functions? What is rate of change, and how do we see it applied to real-life?

  3. Warm-up • Find the slope of the line through (1, 4) and (-5, -2) 2. Find an equation of the line through the pair of points (-2, 5) and (1, -1)

  4. Go over Quiz • 2.1 – 2.4 Quiz

  5. Vocabulary • Scatter Plot- is a graph used to determine whether there is a relationship between paired data.

  6. Correlation Negative Correlation Positive Correlation No correlation As x increases y tends to decrease As x increases y tends to increase The points show no linear pattern

  7. Best Fit Line • When data shows a positive or negative correlation, you can approximate the data with a line. Finding the line that BEST fits the data can be done by hand or by graphing calculator. Today, we will look at how to do it by hand.

  8. Approximating a Best-Fitting Line: Graphical Approach Step 1: Carefully draw a scatter plot of the data. Step 2: Sketch the line that appears to follow most closely the pattern given by 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 two points do not have to be original data points. Step 4: Find an equation of the line that passes through the two points from Step 3. This equation models the data.

  9. Example 1 Example: The data pairs give the number of U.S. births from 1990 to 1997, where x is years since 1990 and y is in thousands. (0,4158) (1,4111) (2,4065) (3, 4000) (4, 3953) (5, 3900) (6, 3891) (7, 3895) • Plot the data points on the graph provided to determine if there is a positive, negative or no correlation of the data. 2. Draw a line that has about equal number of dots below and above the line. 3. Find the equation of the line.

  10. Closure

  11. Homework • Section 2.5 • Page 104 – 105 • #6 – 12, 24, 25

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