1. Math III Accelerated Chapter 11 Data Analysis and Statistics 1

2. Warm Up 11.5  Find the value of y if x = 15. 2

3. 11.5 Modeling Two-Variable Data  Objective:  Create regression equations for data. 3

4. Types of Functions  We use different types of functions to model data.  Given a set of ( x, y ) points, we will use the graphing calculator to create a modeling equation. 4 FunctionGeneral Form Linear y = ax + b Quadratic y = ax 2 + bx + c Cubic y = ax 3 + bx 2 + cx + d Exponential y = ab x Power y = ax b

5. Example 1  The table shows the teacher’s salary y (in dollars) for x years of teaching experience. Write a linear regression equation to model this data.  Enter data into L1 and L2.  Select “4:LinReg” from the STAT CALC menu.  Command: LinReg (ax + b) L1, L2 5 xy 130,624 232,436 334,167 435,989 537,684 639,311 741,098

6. Create a Scatter Plot from ( x, y ) Data  Enter data into L1 and L2.  Select “4:LinReg” from the STAT CALC menu.  Command: LinReg (ax + b) L1, L2, Y1  Use STAT PLOT to configure the graph.  Set WINDOW based on data values.  GRAPH. 6

7. Checkpoint 1  Write a linear regression equation to model this data. 7 x 01234567 y 29192940516173

8. Example 2  The table shows a deer population y counted x years after a hunting ban began. Write an exponential regression equation for this data.  Enter data into L1 and L2.  Select “0:ExpReg” from the STAT CALC menu.  Command: ExpReg L1, L2 8 xy 0500 5729 101271 152206 203765

9. Checkpoint 2  Write an exponential regression equation to model this data. 9 x 1234567 y 462318181107756255

10. Example 3  The table shows the number of people y who rode a roller coaster x hours after an amusement park opened. Write a quadratic regression equation to model this data.  Enter data into L1 and L2.  Select “5:QuadReg” from the STAT CALC menu.  Command: QuadReg L1, L2 10 xy 085 2163 4282 6341 8398 10381 12304

11. Checkpoint 3  Write an quadratic regression equation to model this data. 11 x 024681012 y 100178273314349324289

12. Homework 11.5  Practice 11.5 12