Algebra II Mr. Gilbert Chapter 2.5 Modeling Real-World Data: Using Scatter plots and line of fit Standard & Honors 9/17/2018

Students shall be able to Perform a simple regression, charting results and saving the equation. Use a calculator to determine what kind of equation best models specific data. 9/17/2018

Agenda Warm up Home Work Lesson Practice Homework 9/17/2018

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Homework Review 9/17/2018

Communicate Effectively Line of fit: a line that closely approximates the data points. Prediction Equation: the equation that defines the line of fit. Regression Analysis: a method to find the line of fit. 9/17/2018

Ti-83 Regression types Source:http://academic.pg.cc.md.us/psc/TI83_booklet.pdf 9/17/2018

Example 1 Draw a Scatter Plot Example 2 Find and Use a Prediction Equation 9/17/2018 Lesson 5 Contents

Education The table below shows the approximate percent of students who sent applications to two colleges in various years since 1985. Make a scatter plot of the data. 13 14 15 18 20 Percent 12 9 6 3 Years Since 1985 Source: U.S. News & World Report Graph the data as ordered pairs, with the number of years since 1985 on the horizontal axis and the percentage on the vertical axis. 9/17/2018 Example 5-1a

Safety The table below shows the approximate percent of drivers who wear seat belts in various years since 1994. Make a scatter plot of the data. 73 71 68 69 64 61 58 57 Percent 7 6 5 4 3 2 1 Years Since 1994 Source: National Highway Traffic Safety Administration 9/17/2018 Example 5-1b

Draw a line of fit for the data. How well does the line fit the data? Education The table and scatter plot below show the approximate percent of students who sent applications to two colleges in various years since 1985. Draw a line of fit for the data. How well does the line fit the data? 13 14 15 18 20 Percent 12 9 6 3 Years Since 1985 Source: U.S. News & World Report The points (3, 18) and (15, 13) appear to represent the data well. Draw a line through these two points. 9/17/2018 Example 5-2a

Draw a line of fit for the data. How well does the line fit the data? Education The table and scatter plot below show the approximate percent of students who sent applications to two colleges in various years since 1985. Draw a line of fit for the data. How well does the line fit the data? 13 14 15 18 20 Percent 12 9 6 3 Years Since 1985 Source: U.S. News & World Report Answer: Except for (6, 15), this line fits the data fairly well. 9/17/2018 Example 5-2b

Find a prediction equation. What do the slope and y-intercept indicate? Find an equation of the line through (3, 18) and (15, 13). Begin by finding the slope. Slope formula Substitute. Simplify. 9/17/2018 Example 5-2c

Distributive Property Point-slope form Distributive Property Add 18 to each side. Answer: One prediction equation is The slope indicates that the percent of students sending applications to two colleges is falling at about 0.4% each year. The y-intercept indicates that the percent in 1985 should have been about 19%. 9/17/2018 Example 5-2d

Predict the percent in 2010. The year 2010 is 25 years after 1985, so use the prediction equation to find the value of y when Prediction equation Simplify. Answer: The model predicts that the percent in 2010 should be about 9%. 9/17/2018 Example 5-2e

How accurate is this prediction? Answer: The fit is only approximate, so the prediction may not be very accurate. 9/17/2018 Example 5-2f

Answer: Except for (4, 69), this line fits the data very well. Safety The table and scatter plot show the approximate percent of drivers who wear seat belts in various years since 1994. a. Draw a line of fit for the data. How well does the line fit the data? 73 71 68 69 64 61 58 57 Percent 7 6 5 4 3 2 1 Years Since 1994 Source: National Highway Traffic Safety Administration Answer: Except for (4, 69), this line fits the data very well. 9/17/2018 Example 5-2g

b. Find a prediction equation. What do the slope and b. Find a prediction equation. What do the slope and y-intercept indicate? Answer: Using (1, 58) and (7, 73), an equation is y = 2.5x + 55.5. The slope indicates that the percent of drivers wearing seatbelts is increasing at a rate of 2.5% each year. The y-intercept indicates that, according to the trend of the rest of the data, the percent of drivers who wore seatbelts in 1994 was about 56%. 9/17/2018 Example 5-2h

d. How accurate is the prediction? Answer: 83% c. Predict the percent of drivers who will be wearing seat belts in 2005. d. How accurate is the prediction? Answer: 83% Answer: Except for the outlier, the line fits the data very well, so the predicted value should be fairly accurate. 9/17/2018 Example 5-2i

Homework See Syllabus 2.5 9/17/2018