Analyzing Scatter Plots and Lines of Fit for Student Data

1. Do Now 11/26/18 Copy HW in planner. • Text p. 199, #3-12 all, 14-16 all – answer online • Benchmark Test Chapters 1-4 – Thursday December 5th Plot the following ordered pairs on a graph. The ‘x’ represents hours studying and the ‘y’ represents test scores. Can you draw a line through ALL of the points? If not, is there a pattern to the data. What can you conclude from the graph? (1, 65), (2, 70), (4, 95), (2, 75), (3, 85), (4, 85), (3, 80), (5, 90)

2. 90 80 70 Test scores 60 0 1 2 3 4 5 6 7 Hours of studying (1, 65), (2, 70), (4, 95), (2, 75), (3, 85), (4, 85), (3, 80), (5, 90)

3. Learning Goal • Students will be able to write and solve linear functions, construct scatterplots, analyze lines of fit, and write arithmetic sequences Learning Target • Students will be able to make scatter plots and write equations to model data

4. Section 4.4 “Scatter Plots and Lines of Fit” a graph used to determine whether there is a relationship between paired data. Scatter Plot y x

5. Scatter plots can show trends (patterns) in the data. y y y x x x Relatively no correlation Positive correlation Negative correlation x and y have no apparent relationship. As y tends to increase, x tends to increase. As y tends to decrease, x tends to increase.

6. Make a scatter plot of the data in the table. Describe the correlation of the data. y-axis The scatter plot shows a positive correlation because as x tends to increase, y tends to increase. 4 3 2 1 x-axis 0 1 2 3 4 5 6 7

7. Make a scatter plot of the data in the table. Describe the correlation of the data. y-axis The scatter plot shows a negative correlation because as minutes on the treadmill increase, ounces of water in the water bottle decreases. 12 8 Ounces of water in water bottle 4 x-axis 0 5 10 15 20 25 30 35 Minutes on the treadmill

8. Modeling Data When data show a positive or negative correlation, you can model the trend in the data using a LINE OF FIT Make a scatter plot of the data. Decide whether the data can be a modeled by a line. (Does it have positive or negative correlation?) Draw a line that appears to fit the data closely. Write an equation using two points on the line. (The points do not have to be actual data pairs, but they do have to be on the line.)

9. Draw a line of fit for the scatter plot. Write an equation that models the number of ounces of water left in the water bottle as a function of minutes on the treadmill. Write an equation using two points on the line. y-axis 12 Use the points (5,12) and (30,4). 12 – 4 = _8_ 5 – 30 -25 8 Ounces of water in water bottle Find the y-intercept. Use (5,12). 4 y = mx + b 12 = 8 (5) + b b = 68 -25 5 0 5 10 15 20 25 30 35 x-axis y = 8 x + 68 -25 5 Minutes on the treadmill

10. Draw a line of fit for the scatter plot. Write an equation that models the number of years since 2000 as a function student enrollment. Years since 2000 Enrollment Enrollment at Howell Middle School South Write an equation using two points on the line. 950 940 Use the points (4, 900) and (6, 910). 930 910 – 900 = _10_ = 5 6 – 4 2 920 Student enrollment 910 Find the y-intercept. Use (4, 900). 900 y = mx + b 900 = 5(4) + b b = 880 890 880 x-axis y = 5x + 880 00 01 02 03 04 05 06 07 08 09 year

11. What Did You Learn Today? Scatter Plot LINE OF FIT Negative correlation Positive correlation Relatively no correlation

12. Homework • Text p. 199, #3-12 all, 14-16 all