1. Regression Math 12

2. Regression You can use this when the question does not specify that you must solve “algebraically” You can use regression when you have: A sequence or a table of values You will want to use this when you are given data values but no equation. Regression will give you the equation

3. Set Up Your Calculator Make sure diagnostic is turned on, on your graphing calculator (this will produce R 2 ) “2 nd” “0” “matrix” “diagnostic on” “enter” “enter” Hit clear R 2 can be anywhere between 0 and 1 (we will only deal with functions that have a R 2 = 1 When R 2 = 1 you have a perfect function (it hits every point on the graph)

4. Graphs Draw scatterplots to show: It hits every point on the graph therefore R 2 =1 Scatterplot where there is a line of best fit R 2 = less than one (ex. 0.83)

5. Let’s Find an Equation Using Regression!!! Here are your points: n12345 tntn 23456

6. Steps to Find an Equation Using Regression The first thing you have to do is determine if this is a linear, quadratic, or cubic (find common difference – 1 st level is arithmetic, 2 nd is quadratic and 3 rd is cubic) You should find that this is linear On your graphing calculator hit “stat” “edit” then enter your data (make sure that in list 1 (L1) you have the n values and in List 2 (L2) you have the t n values). If you have data that is already there DO NOT HIT DELETE!!!!!!!!!!!!!!!! This will delete the whole list and you will have to clear your entire calculator and start over. Instead select the L1 and hit clear or type over old numbers (making sure no old numbers remain).

7. Steps to Find an Equation Using Regression Once you have the data entered into L1 and L2 hit “stat” “calc” “LinReg” “enter” “enter” This is your equation! It tells you the format of the equation and the value of each variable (except for x and y) We will always have R 2 = 1 and R = 1 (this means it is a perfect function)

8. Answer: Using the information on your graphing calculator you should be able to see that the equation is y = 1x + 1 or y = x + 1

9. Let’s Do Another! n1234 tntn 24711

10. Steps to Find an Equation Using Regression The first thing you have to do is determine if this is a linear, quadratic, or cubic (find common difference – 1 st level is arithmetic, 2 nd is quadratic and 3 rd is cubic) You should find that this is quadratic On your graphing calculator hit “stat” “edit” then enter your data (make sure that in list 1 (L1) you have the n values and in List 2 (L2) you have the t n values). If you have data that is already there DO NOT HIT DELETE!!!!!!!!!!!!!!! Instead hit clear or type over old numbers (making sure no old numbers remain).

11. Steps to Find an Equation Using Regression Once you have the data entered into L1 and L2 hit “stat” “calc” “QuadReg” “enter” “enter” This is your equation! It tells you the format of the equation and the value of each variable (except for x and y) Plug these values into the quadratic equation and that is your answer.

12. Answer: Your equation should be: Y = 0.5x 2 + 0.5x + 1 Note: If you are given sequences you should write your equation in terms of t n and n.

13. You Can Try This One on Your Own n1234 tntn -5-6-11-20

14. Answer: Y = -2x 2 +5x -8 Unit Test Monday Complete Sheet 15 for homework if you don’t finish