3 9 Curve Fitting with Polynomials

Transcription

1 3 9 Curve Fitting with Polynomials Relax! You will do fine today! We will review for quiz!!! (which is worth 10 points, has 20 questions, group, graphing calculator allowed, and will not be on your first quarter grades) warm up 3 9 Curve Fitting with Polynomials 1. Use finite differences to determine the degree of a polynomial that will fit a given set of data. 2. Use technology to find models. To predict We will also review for quiz!!! Learning Target 1

2 How to do a regression equation on your calculator: 1. Note: if you want to find r, the correlation coefficient, you will need to turn your Diagnostics On. This is a one time thing. To this, press 2 nd and the on button which will get you to the catalog. Then scroll down to the DiaGnosticOn option. Push enter, then enter again. 2. Enter in your data: a. Push the STAT button b. Select 1:Edit and push enter c. Enter your data into L1 and L2 3. Calculate your line/parabola/etc.: a. Push the STAT button again b. Arrow over to CALC c. Choose the appropriate regression (#4. LinReg if you want to find a linear regression equation Regression Eq. How to Graph Data: 1. Enter in your data: a. Push the STAT button b. Select 1:Edit and push enter c. Enter your data into L1 and L2 2. Set up your graph: a. Push the STAT PLOT button (2 nd Y=) b. Select 1:Plot 1 and push enter c. Turn on by pushing enter on the word On d. Select type (dotted) e. Check Xlist: L 1, f. Check Ylist: L 2 3. Set up your window: a. Push the WINDOW button b. Set your x values to include all of your data values in the x table c. Set your y values to include all of your data values in the y table d. Xscl and Yscl should be appropriate for the data 4. Graph your data: Just push GRAPH Graph Data 2

3 How to insert a regression equation into Y 1 1. Enter data into list 1 and list 2 (see how to calculate a regression equation ) 2. Calculate a regression equation (see how to calculate a regression equation ) Note: your Homescreen will now have the regression equation 3. Select the Y= button 4. At the Y 1 screen, select VARS 5. Choose 5. Statistics 6. Arrow over to EQ 7. Select 1: RegEQ You should now have the regression equation you calculated in your Y 1 Insert a regression How to find a value of a function that is in Y 1 given the x value 1. You could graph and use trace until you get around the x value then look at y 2. You could go to the table and search the x values to find the y value 3. You could go to table set TBLSET and set the TblStart to the x value, then look at the table 4. OR Go to the homescreen 5. Press VARS 6. Arrow over to Y VARS 7. Select 1:Function 8. Select 1: Y 1 or wherever your function resides 9. Now Y 1 shows up on the homescreen. 10. Type a ( and the x value of choice. You could finish it with a ) 11. Push enter Example: Y 1 = 8x + 3 Y 1 (5) enter 43 Finding a value 3

4 I. Using Finite Differences 1. Use finite differences to determine the degree of the polynomial that best describes the data. The x values increase by a constant 2. Find the differences of the y values. First differences: Not constant Second differences: Not constant Third differences: Constant The third differences are constant. A cubic polynomial best describes the data Use finite differences to determine the degree of the polynomial that best describes the data. The x values increase by a constant 3. Find the differences of the y values. First differences: Not constant Second differences: Not constant Third differences: Not constant Fourth differences: 3 3 Constant You try 4

5 II. Use Differences for Real Data 4. The table below shows the population of a city from 1960 to Write a polynomial function for the data. First differences: Second differences: Third differences: Close f(x) 0.10x x x The table below shows the gas consumption of a compact car driven a constant distance at various speed. Write a polynomial function for the data. First differences: Second differences: Third differences: Close f(x) 0.001x x x you try 5

6 Helpful Hint Often, real world data can be too irregular for you to use finite differences or find a polynomial function that fits perfectly. In these situations, you can use the regression feature of your graphing calculator. Remember that the closer the R 2 value is to 1, the better the function fits the data. Helpful Hint III. Using the Regression Feature 6. The table below shows the opening value of a stock index on the first day of trading in various years. Use a polynomial model to estimate the value on the first day of trading in Step 1: enter data in the calculator Step 2: graph data to help with guesses Step 3: compute different regressions, check R 2 cubic: R quartic: R The quartic function is more appropriate choice. f(x) = 32.23x x x x Step 4: Answer the question 2000 is 6 years after Substitute 6 for x in the quartic model: f(6) = 32.23(6) (6) (6) (6) Based on the model, the opening value was about $ in

7 3.9 p.213 #1 5, 7 17 odd, 18, *15 problems Review for Quiz Next Slide... Homework 3.1 Polynomials add/sub/identify 3.2 Multiplying Polynomials & Pascal 3.3 Dividing Polynomials synthetic/long division 3.4 Factoring Polynomials 3.5 Finding Real Roots (solving) 3.6 Fundamental Theorem of Algebra 3.7 Graphing Polynomials 3.8 Transforming Polynomial Functions *3.9 Curve Fitting (regression) snapshot of chapter 7

8 3.1 Polynomials add/sub/identify 3.2 Multiplying Polynomials & Pascal 3.3 Dividing Polynomials synthetic/long division Factoring Polynomials 3.5 Finding Real Roots (solving) 3.6 Fundamental Theorem of Algebra

9 3.7 Graphing Polynomials 3.8 Transforming Polynomial Functions *3.9 Curve Fitting (regression)