1.6 Using Data to Predict

1. Chapter 1 Math 10 Ms. Albarico 1.6 Using Data to Predict

2. Students are expected to: • Analyze graphs or charts of given situations to identify information. • Create and analyze scatter plots, using appropriate technology. • Construct and analyze graphs and tables relating two variables. • Develop and apply strategies for solving problems. • Solve problems using graphing technology • Determine and apply a line of best fit, using the least-squares method and median-median method, with and without technology, and describe the differences between the two methods. • Demonstrate an intuitive understanding of correlation. • Use interpolation, extrapolation, and equations to predict and solve problems

3. Vocabulary • Predict(v) • Join(v) • Arrangement • Corresponds(v)

4. Scatter Plots and Lines of Best Fit Key Terms: Scatter Plot – a graph of plotted Ordered pairs that represents the relationship Between two variables. Line of best fit – line used in scatter plots to show a trend in data.

5. Input these data in your calculator: What is the a) dependent variable? b) independent variable? Domain - ? Range - ?

6. Domain and Range What is the a) dependent variable? Mean height b) independent variable? Age (years) Domain - The domain of a function is the set of all possible input values (usually x). Range - The range is the set of all possible output values (usually y).

7. Your graph should look like this:

8. Calculator Commands • Press Window • Xmin = 0 • Xmax=10 • Xscl=2 • Ymin=0 • Ymax=150 • Yscl=20 • Xres=1 Enter the data into your list. Make sure you can identify which list is your x values and y values. 2) Adjust the setting of your calculator’s window. 3) Turn the STAT PLOTS ( 2nd Y=). 4) Make sure the ON text is blinking. 5) Scroll down and choose what type of plot. Choose Type 1 for scatter plot. 6) Enter which list is your x values then your Y list. 7) Press GRAPH.

9. Calculator Command for Line of Best Fit • Display • y= ax + b • a= 10 • b= 23 • Equation is: • y= 10x + 23 Part 1 Press STAT. 2) Press right arrow (). It should be at CALC function. 3) If the ordered pairs form a straight line, press #4. If the plotted pairs are does not form a straight line, choose # 3. 4) Enter your X list and Y list. 5) Press ENTERENTER. 6) The display window will show you an equation. 7) Write down this equation in your notebook. Part 2 Press Y=. Enter the equation you generate from Part 1. Press GRAPH.

10. Key Terms Discrete data – all values in the graph that is not meaningful and it can’t be joined. Continuous data - all values in the graph that is meaningful that can be joined. Interpolate- make a prediction that falls between given pieces of data. Extrapolate – make a prediction that is outside the range of given values.

11. Example:

12. Example: The cost of CDs is plotted for each CD you purchase. The cost to you changes only when another CD is purchased. The values between the plotted points are not meaningful and therefore are not joined. This is discrete data. The amount of fuel remaining in your gas tank is plotted for each hour you drive. However, the amount of fuel in your gas tank decreases every minute/second you drive. All values on the graph are meaningful and therefore can be joined. This is continuous data.

13. Let’s make a prediction!

14. Finding Unknown x values: Make sure your window will enclose the unknown value you are going to find. 2) Press 2ndTRACE. 3) Choose #1. 4) Enter a value( for example x =10). 5) Press ENTER. 6) The display window will show the value of y.

15. Practice Exercise: • Answer CYU # 6 & 7 • Next Meeting: (Case Study 2 and Chapter Reflection) • Bring the following materials: • A scrap piece of cloth • Thread • Pen, nut , or bolt ( You are going to make a parachute.)

16. Weekend Homework (Notebook) Case Study 1 & Extension 1 on pages 44-45. www.ilovemathisfun.weebly.com